It has been known that determining the exact value of vertex distinguishing edge index X ＇8（G） of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete...It has been known that determining the exact value of vertex distinguishing edge index X ＇8（G） of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete, graphs, and graphs with maximum degree 2. Let rid（G） denote the number of vertices of degree d in G, and let X＇es（G） be the equitable vertex distinguishing edge index of G. We show that a tree T holds nl （T） ≤ X ＇s （T） ≤ n1 （T） ＋ 1 and X＇s（T） = X＇es（T） if T satisfies one of the following conditions （i） n2（T） ≤△（T） or （ii） there exists a constant c with respect to 0 〈 c 〈 1 such that n2（T） △ cn1（T） and ∑3 ≤d≤△（T）nd（T） ≤ （1 - c）n1（T） ＋ 1.展开更多
For any graph G, the Inj-equitable graph of a graph G, denoted by IE (G) , is the graph with the same vertices as G and for any two adjacent vertices u and v in IE (G), ≤ 1, where for any vertex w∈V (G) , degin (w)?...For any graph G, the Inj-equitable graph of a graph G, denoted by IE (G) , is the graph with the same vertices as G and for any two adjacent vertices u and v in IE (G), ≤ 1, where for any vertex w∈V (G) , degin (w)?= . In this paper, Inj-equitable graphs of some graphs are obtained, and some properties and results are established. Moreover, complete Inj-equitable graph and the Inj-equitable graph are defined.展开更多
Let G be a graph with p vertices and q edges and let A= vertex labeling is said to be a vertex equitable labeling of G if it induces an edge labeling given by such that and , where is the number of vertices v with for...Let G be a graph with p vertices and q edges and let A= vertex labeling is said to be a vertex equitable labeling of G if it induces an edge labeling given by such that and , where is the number of vertices v with for A graph G is said to be a vertex equitable graph if it admits vertex equitable labeling. In this paper, we establish the vertex equitable labeling of a Tp-tree, where T is a Tp-tree with even number of vertices, bistar the caterpillar and展开更多
Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G)...Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G) and (u, v) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.展开更多
A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominatin...A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominating set is denoted by and is called the Inj-equitable domination number of G. In this paper, we introduce the injective equitable domination of a graph and study its relation with other domination parameters. The minimal injective equitable dominating set, the injective equitable independence number , and the injective equitable domatic number are defined.展开更多
A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equit...A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equitable total chromatic?number. In this paper, we prove some theorems on equitable?total coloring and derive the equitable total chromatic numbers?of Pm V?Sn, Pm V?Fn and Pm V Wn.展开更多
Somalia is a country facing numerous challenges in achieving universal health coverage (UHC) and ensuring adequate healthcare financing, This article explores the complexities and obstacles that Somalia must overcome ...Somalia is a country facing numerous challenges in achieving universal health coverage (UHC) and ensuring adequate healthcare financing, This article explores the complexities and obstacles that Somalia must overcome in its pursuit of UHC, the paper begins by providing an overview of the current healthcare landscape in Somalia, highlighting the lack of infrastructure, political instability, and limited financial resources that hinder the establishment of a comprehensive and equitable healthcare system. It then examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while emphasizing the need for a more sustainable, domestically financed solution. Drawing on a range of data sources and case studies, the article proposes a multi-faceted approach to strengthen healthcare governance, improve resource allocation, and foster local capacity building, the study delves into the unique obstacles that Somalia faces, including a lack of infrastructure, political instability, and limited financial resources, which hinder the establishment of a comprehensive and equitable healthcare system. The paper also examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while highlighting the need for a more sustainable, domestically financed solution. The findings underscore the importance of political commitment, international cooperation, and innovative financing mechanisms in advancing towards UHC in Somalia, providing valuable insights for other low resource, conflict affected settings.展开更多
A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible.In this paper,we give new methods to prove some known results of equitable coloring of com...A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible.In this paper,we give new methods to prove some known results of equitable coloring of complete r-partite Graphs.展开更多
Private security companies through the services they provide complement the police in crime prevention, order maintenance, and general improvement of security in societies thereby contributing to sustainable national ...Private security companies through the services they provide complement the police in crime prevention, order maintenance, and general improvement of security in societies thereby contributing to sustainable national development In order to fully benefit from their contribution and prevent them from engaging in illegal activities, states formulate and enforce policies that seek to regulate their activities. This paper examines the regulation of private guards companies in Nigeria using Abuja as its empirical core. The main aim is to promote understanding of how the private security industry is regulated and evaluate the effectiveness of the existing regulatory policy. Data for the paper were generated from in-depth interviews with the NSCDC （Nigeria Security and Civil Defence Corps）, analysis of the policy for PSCs （private security companies）, and a review of the annual performance report of the regulatory agency. The results revealed that the current system of PSC regulation is characterized by a lack of specialty classification of private security licences, limited regulatory scope with a focus on licensing of companies, lack of uniform standards on training, and high cost/difficulties in obtaining operational license. The paper concludes that the current regulatory setup for PSCs in Nigeria is ineffective and unsustainable and recommends an urgent review of the legal framework to alien its provisions with global standards and practices in the private security industry.展开更多
Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between ve...Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.展开更多
The China Railway Express(CRE)has improved regional economic integration with external markets and has reshaped regional development by encouraging the relocation of manufacturing activities("manufacturing transf...The China Railway Express(CRE)has improved regional economic integration with external markets and has reshaped regional development by encouraging the relocation of manufacturing activities("manufacturing transfer").We analyzed data from 284 prefecture-level cities in China to evaluate the impact of the CRE on regional manufacturing relocation,using a staggered difference-in-diferences model with entropy balancing.We found that the launch of the CRE significantly stimulated the relocation of manufacturing industries to node cities-key hubs for transportation and logistics within the CRE network-especially in the central,western,and northeastern regions.Specifically,the CRE significantly increased manufacturing dynamism,firm profitability,openness,and foreign investment in node cities,which attracted more manufacturing industries to relocate in this area.Higher levels of infrastructure development moderated the CRE's effect.Further analysis showed that significant moderating effects of infrastructure development occurred only in the western region.Overall,our conclusions provide useful insights into how to promote equitable regional development through manufacturing development in China.展开更多
This editorial,comments on the article by Spartalis et al published in the recent issue of the World Journal of Cardiology.We here provide an outlook on potential ethical concerns related to the future application of ...This editorial,comments on the article by Spartalis et al published in the recent issue of the World Journal of Cardiology.We here provide an outlook on potential ethical concerns related to the future application of gene therapy in the field of inherited arrhythmias.As monogenic diseases with no or few therapeutic options available through standard care,inherited arrhythmias are ideal candidates to gene therapy in their treatment.Patients with inherited arrhythmias typically have a poor quality of life,especially young people engaged in agonistic sports.While genome editing for treatment of inherited arrhythmias still has theoretical application,advances in CRISPR/Cas9 technology now allows the generation of knock-in animal models of the disease.However,clinical translation is somehow expected soon and this make consistent discussing about ethical concerns related to gene editing in inherited arrhythmias.Genomic off-target activity is a known technical issue,but its relationship with ethnical and individual genetical diversity raises concerns about an equitable accessibility.Meanwhile,the costeffectiveness may further limit an equal distribution of gene therapies.The economic burden of gene therapies on healthcare systems is is increasingly recognized as a pressing concern.A growing body of studies are reporting uncertainty in payback periods with intuitive short-term effects for insurance-based healthcare systems,but potential concerns for universal healthcare systems in the long term as well.Altogether,those aspects strongly indicate a need of regulatory entities to manage those issues.展开更多
Highlights Among the East Asian nations,a recurring predicament faced by educational institutions is that of providing inclusive but high-quality education.Active involvement of non-governmental organizations(NGOs)in ...Highlights Among the East Asian nations,a recurring predicament faced by educational institutions is that of providing inclusive but high-quality education.Active involvement of non-governmental organizations(NGOs)in education is valuable in China.Adream was such an NGO on education in China,established in 2008 with a singular and noble objective:promotion of equitable access to quality education within the disadvantaged regions of China.展开更多
基金supported by the National Natural Science Foundation of China (61163054),supported by the National Natural Science Foundation of China (61163037)
文摘It has been known that determining the exact value of vertex distinguishing edge index X ＇8（G） of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete, graphs, and graphs with maximum degree 2. Let rid（G） denote the number of vertices of degree d in G, and let X＇es（G） be the equitable vertex distinguishing edge index of G. We show that a tree T holds nl （T） ≤ X ＇s （T） ≤ n1 （T） ＋ 1 and X＇s（T） = X＇es（T） if T satisfies one of the following conditions （i） n2（T） ≤△（T） or （ii） there exists a constant c with respect to 0 〈 c 〈 1 such that n2（T） △ cn1（T） and ∑3 ≤d≤△（T）nd（T） ≤ （1 - c）n1（T） ＋ 1.
文摘For any graph G, the Inj-equitable graph of a graph G, denoted by IE (G) , is the graph with the same vertices as G and for any two adjacent vertices u and v in IE (G), ≤ 1, where for any vertex w∈V (G) , degin (w)?= . In this paper, Inj-equitable graphs of some graphs are obtained, and some properties and results are established. Moreover, complete Inj-equitable graph and the Inj-equitable graph are defined.
文摘Let G be a graph with p vertices and q edges and let A= vertex labeling is said to be a vertex equitable labeling of G if it induces an edge labeling given by such that and , where is the number of vertices v with for A graph G is said to be a vertex equitable graph if it admits vertex equitable labeling. In this paper, we establish the vertex equitable labeling of a Tp-tree, where T is a Tp-tree with even number of vertices, bistar the caterpillar and
文摘Let G= (V, E) be a graph and A(G) is the collection of all minimal equitable dominating set of G. The middle equitable dominating graph of G is the graph denoted by Med(G) with vertex set the disjoint union of V∪A(G) and (u, v) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.
文摘A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominating set is denoted by and is called the Inj-equitable domination number of G. In this paper, we introduce the injective equitable domination of a graph and study its relation with other domination parameters. The minimal injective equitable dominating set, the injective equitable independence number , and the injective equitable domatic number are defined.
文摘A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equitable total chromatic?number. In this paper, we prove some theorems on equitable?total coloring and derive the equitable total chromatic numbers?of Pm V?Sn, Pm V?Fn and Pm V Wn.
文摘Somalia is a country facing numerous challenges in achieving universal health coverage (UHC) and ensuring adequate healthcare financing, This article explores the complexities and obstacles that Somalia must overcome in its pursuit of UHC, the paper begins by providing an overview of the current healthcare landscape in Somalia, highlighting the lack of infrastructure, political instability, and limited financial resources that hinder the establishment of a comprehensive and equitable healthcare system. It then examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while emphasizing the need for a more sustainable, domestically financed solution. Drawing on a range of data sources and case studies, the article proposes a multi-faceted approach to strengthen healthcare governance, improve resource allocation, and foster local capacity building, the study delves into the unique obstacles that Somalia faces, including a lack of infrastructure, political instability, and limited financial resources, which hinder the establishment of a comprehensive and equitable healthcare system. The paper also examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while highlighting the need for a more sustainable, domestically financed solution. The findings underscore the importance of political commitment, international cooperation, and innovative financing mechanisms in advancing towards UHC in Somalia, providing valuable insights for other low resource, conflict affected settings.
文摘A graph is equitably k-colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible.In this paper,we give new methods to prove some known results of equitable coloring of complete r-partite Graphs.
文摘Private security companies through the services they provide complement the police in crime prevention, order maintenance, and general improvement of security in societies thereby contributing to sustainable national development In order to fully benefit from their contribution and prevent them from engaging in illegal activities, states formulate and enforce policies that seek to regulate their activities. This paper examines the regulation of private guards companies in Nigeria using Abuja as its empirical core. The main aim is to promote understanding of how the private security industry is regulated and evaluate the effectiveness of the existing regulatory policy. Data for the paper were generated from in-depth interviews with the NSCDC （Nigeria Security and Civil Defence Corps）, analysis of the policy for PSCs （private security companies）, and a review of the annual performance report of the regulatory agency. The results revealed that the current system of PSC regulation is characterized by a lack of specialty classification of private security licences, limited regulatory scope with a focus on licensing of companies, lack of uniform standards on training, and high cost/difficulties in obtaining operational license. The paper concludes that the current regulatory setup for PSCs in Nigeria is ineffective and unsustainable and recommends an urgent review of the legal framework to alien its provisions with global standards and practices in the private security industry.
文摘Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.
基金support from the National Social Science Fund of China (No.22BGJ049)the National Natural Science Foundation of China (No.72174056).
文摘The China Railway Express(CRE)has improved regional economic integration with external markets and has reshaped regional development by encouraging the relocation of manufacturing activities("manufacturing transfer").We analyzed data from 284 prefecture-level cities in China to evaluate the impact of the CRE on regional manufacturing relocation,using a staggered difference-in-diferences model with entropy balancing.We found that the launch of the CRE significantly stimulated the relocation of manufacturing industries to node cities-key hubs for transportation and logistics within the CRE network-especially in the central,western,and northeastern regions.Specifically,the CRE significantly increased manufacturing dynamism,firm profitability,openness,and foreign investment in node cities,which attracted more manufacturing industries to relocate in this area.Higher levels of infrastructure development moderated the CRE's effect.Further analysis showed that significant moderating effects of infrastructure development occurred only in the western region.Overall,our conclusions provide useful insights into how to promote equitable regional development through manufacturing development in China.
文摘This editorial,comments on the article by Spartalis et al published in the recent issue of the World Journal of Cardiology.We here provide an outlook on potential ethical concerns related to the future application of gene therapy in the field of inherited arrhythmias.As monogenic diseases with no or few therapeutic options available through standard care,inherited arrhythmias are ideal candidates to gene therapy in their treatment.Patients with inherited arrhythmias typically have a poor quality of life,especially young people engaged in agonistic sports.While genome editing for treatment of inherited arrhythmias still has theoretical application,advances in CRISPR/Cas9 technology now allows the generation of knock-in animal models of the disease.However,clinical translation is somehow expected soon and this make consistent discussing about ethical concerns related to gene editing in inherited arrhythmias.Genomic off-target activity is a known technical issue,but its relationship with ethnical and individual genetical diversity raises concerns about an equitable accessibility.Meanwhile,the costeffectiveness may further limit an equal distribution of gene therapies.The economic burden of gene therapies on healthcare systems is is increasingly recognized as a pressing concern.A growing body of studies are reporting uncertainty in payback periods with intuitive short-term effects for insurance-based healthcare systems,but potential concerns for universal healthcare systems in the long term as well.Altogether,those aspects strongly indicate a need of regulatory entities to manage those issues.
文摘Highlights Among the East Asian nations,a recurring predicament faced by educational institutions is that of providing inclusive but high-quality education.Active involvement of non-governmental organizations(NGOs)in education is valuable in China.Adream was such an NGO on education in China,established in 2008 with a singular and noble objective:promotion of equitable access to quality education within the disadvantaged regions of China.
