Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC in...Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC index for short） of a graph G is defined asABC（G） =∑uv∈E（G）(（d;+ d;-2）/d;d;),where d;and d;denote the degree of vertices u and v in G,respectively.In this paper,trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined,respectively.展开更多
The augmented Zagreb index displays a good correlation with the formation heat of octanes and heptanes. The augmented Zagreb index of catacondensed hexagonal systems and molecular trees was discussed. By using the met...The augmented Zagreb index displays a good correlation with the formation heat of octanes and heptanes. The augmented Zagreb index of catacondensed hexagonal systems and molecular trees was discussed. By using the methods of analysis of graph structure and mathematical induction,the catacondensed hexagonal systems with extreme augmented Zagreb index were characterized.The lower bound for augmented Zagreb index of molecular trees with fixed numbers of pendent vertices was given,and the extremal trees were characterized. From these results,we can compare the formation heat of catacondensed hexagonal systems and molecular trees.展开更多
Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</...Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</sub>(G,x) and Zg<sub>1</sub>(G) of the graph G are defined as Σ<sub>uv∈E(G)</sub>x<sup>(d<sub>u</sub>+d<sub>v</sub>)</sup> and Σ<sub>e=uv∈E(G)</sub>(d<sub>u</sub>+d<sub>v</sub>) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg<sub>1</sub>*</sup>=Σ<sub>uv∈E(G)</sub>(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.展开更多
In this note, we correct a wrong result in a paper of Das et al. with regard to the comparison between the Wiener index and the Zagreb indices for trees （Das K C, Jeon H, Trinajstic N. The comparison between the Wie...In this note, we correct a wrong result in a paper of Das et al. with regard to the comparison between the Wiener index and the Zagreb indices for trees （Das K C, Jeon H, Trinajstic N. The comparison between the Wiener index and the Zagreb indices and the eccentric connectivity index for trees. Discrete Appl. Math., 2014, 171：35 41）, and give a simple way to compare the Wiener index and the Zagreb indices for trees. Moreover, the comparison between the Wiener index and the Zagreb indices for unicyclic graphs is carried out.展开更多
In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemic...In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube, nanostar and polyomino chain.展开更多
Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its compleme...Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its complement respectively.Lanzhou index Lz(G)can be expressed as(n-1)M_(1)(G)-F(G),where M_(1)(G)and F(G)denote the first Zagreb index and the forgotten index of G respectively,and n is the number of vertices in G.It turns out that Lanzhou index outperforms M_(1)(G)and F(G)in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers.It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively.In this paper,we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately.展开更多
文摘Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC index for short） of a graph G is defined asABC（G） =∑uv∈E（G）(（d;+ d;-2）/d;d;),where d;and d;denote the degree of vertices u and v in G,respectively.In this paper,trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined,respectively.
基金National Natural Science Foundation of China(No.11071227)Shanxi Scholarship Council of China(No.2012-070)Foundation of North University of China(No.2013-12-1)
文摘The augmented Zagreb index displays a good correlation with the formation heat of octanes and heptanes. The augmented Zagreb index of catacondensed hexagonal systems and molecular trees was discussed. By using the methods of analysis of graph structure and mathematical induction,the catacondensed hexagonal systems with extreme augmented Zagreb index were characterized.The lower bound for augmented Zagreb index of molecular trees with fixed numbers of pendent vertices was given,and the extremal trees were characterized. From these results,we can compare the formation heat of catacondensed hexagonal systems and molecular trees.
文摘Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</sub>(G,x) and Zg<sub>1</sub>(G) of the graph G are defined as Σ<sub>uv∈E(G)</sub>x<sup>(d<sub>u</sub>+d<sub>v</sub>)</sup> and Σ<sub>e=uv∈E(G)</sub>(d<sub>u</sub>+d<sub>v</sub>) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg<sub>1</sub>*</sup>=Σ<sub>uv∈E(G)</sub>(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.
基金The NSF(11301093,11501139)of Chinathe NSF(2014A030313640)of Guangdong Provincethe Foundation(Yq2014111)for Distinguished Young Talents in Higher Education of Guangdong Province
文摘In this note, we correct a wrong result in a paper of Das et al. with regard to the comparison between the Wiener index and the Zagreb indices for trees （Das K C, Jeon H, Trinajstic N. The comparison between the Wiener index and the Zagreb indices and the eccentric connectivity index for trees. Discrete Appl. Math., 2014, 171：35 41）, and give a simple way to compare the Wiener index and the Zagreb indices for trees. Moreover, the comparison between the Wiener index and the Zagreb indices for unicyclic graphs is carried out.
文摘In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube, nanostar and polyomino chain.
基金Supported by the National Natural Science Foundation of China(11871256)the Chinese-Croatian bilateral project(7-22)。
文摘Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its complement respectively.Lanzhou index Lz(G)can be expressed as(n-1)M_(1)(G)-F(G),where M_(1)(G)and F(G)denote the first Zagreb index and the forgotten index of G respectively,and n is the number of vertices in G.It turns out that Lanzhou index outperforms M_(1)(G)and F(G)in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers.It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively.In this paper,we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately.
基金Supported by Talent Introduction Project of Anhui Science and Technology University(XWYJ201801)the Research Project of Chizhou University(2015ZR005+3 种基金2016ZR0082016XJXTD022017ZRZ009)the Project of the Outstanding Young Talent Support Program of the Universities of Anhui Province(gxyq2019107)
