A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S...A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)~2,S_(12)~2,S_(12)~4,S_(12)~5,S_(14)~3,S_(14)~5,S_(16)~3,S_(18)~5,S_(24) as shown in Fig.1.As a corollary,it is shown that if a {(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.展开更多
A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of ...A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)展开更多
In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this proble...In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.展开更多
With the rapid growth in the availability of digital health-related data,there is a great demand for the utilization of intelligent information systems within the healthcare sector.These systems can manage and manipul...With the rapid growth in the availability of digital health-related data,there is a great demand for the utilization of intelligent information systems within the healthcare sector.These systems can manage and manipulate this massive amount of health-related data and encourage different decision-making tasks.They can also provide various sustainable health services such as medical error reduction,diagnosis acceleration,and clinical services quality improvement.The intensive care unit(ICU)is one of the most important hospital units.However,there are limited rooms and resources in most hospitals.During times of seasonal diseases and pandemics,ICUs face high admission demand.In line with this increasing number of admissions,determining health risk levels has become an essential and imperative task.It creates a heightened demand for the implementation of an expert decision support system,enabling doctors to accurately and swiftly determine the risk level of patients.Therefore,this study proposes a fuzzy logic inference system built on domain-specific knowledge graphs,as a proof-of-concept,for tackling this healthcare-related issue.The system employs a combination of two sets of fuzzy input parameters to classify health risk levels of new admissions to hospitals.The proposed system implemented utilizes MATLAB Fuzzy Logic Toolbox via several experiments showing the validity of the proposed system.展开更多
基金Supported by NSFC(Grant Nos.11801148 and 11626089)the Foundation for the Doctor of Henan Polytechnic University(Grant No.B2014-060)。
文摘A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)~2,S_(12)~2,S_(12)~4,S_(12)~5,S_(14)~3,S_(14)~5,S_(16)~3,S_(18)~5,S_(24) as shown in Fig.1.As a corollary,it is shown that if a {(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.
基金Supported by the National Natural Science Foundation of China（11171273） Supported by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical Uni- versity（Z2016170）
文摘A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)
基金support from FCT—Fundacao para a Ciencia e a Tecnologia(Portugal),through Projects PTDC/MAT/113207/2009PEst-OE/MAT/UI0297/2011(CMA).
文摘In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.
基金funded by the Deanship of Scientific Research at Umm Al-Qura University,Makkah,Kingdom of Saudi Arabia.Under Grant Code:22UQU4281755DSR05.
文摘With the rapid growth in the availability of digital health-related data,there is a great demand for the utilization of intelligent information systems within the healthcare sector.These systems can manage and manipulate this massive amount of health-related data and encourage different decision-making tasks.They can also provide various sustainable health services such as medical error reduction,diagnosis acceleration,and clinical services quality improvement.The intensive care unit(ICU)is one of the most important hospital units.However,there are limited rooms and resources in most hospitals.During times of seasonal diseases and pandemics,ICUs face high admission demand.In line with this increasing number of admissions,determining health risk levels has become an essential and imperative task.It creates a heightened demand for the implementation of an expert decision support system,enabling doctors to accurately and swiftly determine the risk level of patients.Therefore,this study proposes a fuzzy logic inference system built on domain-specific knowledge graphs,as a proof-of-concept,for tackling this healthcare-related issue.The system employs a combination of two sets of fuzzy input parameters to classify health risk levels of new admissions to hospitals.The proposed system implemented utilizes MATLAB Fuzzy Logic Toolbox via several experiments showing the validity of the proposed system.
