For a connected simple graph G, the eccentricity ec（v） of a vertex v in G is the distance from v to a vertex farthest from v, and d（v） denotes the degree of a vertex v. The eccentric connectivity index of G, denot...For a connected simple graph G, the eccentricity ec（v） of a vertex v in G is the distance from v to a vertex farthest from v, and d（v） denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξC（G）, is defined as ∑vЕV（G） d（v）ec（v）. In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges（n ≤ m ≤ n ＋ 4）, and propose a conjecture on the graphs with maximal eccentric connectivity index and m edges （m ≥ n ＋ 5）. among the connected graphs with n vertices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
The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentri...The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentricity have a wide range of applications in structure-activity relationships and pharmaceutical drug design etc. In this paper, we investigate the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene. We find a relation between the radius and the number of spokes of a (3, 6)-fullerene. Based on the relation, we give the computing formulas of the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene, respectively.展开更多
基金Supported by China Postdoctoral Science Foundation(2012M520815 and 2013T60411)the National Natural Science Foundation of China(11001089)
文摘For a connected simple graph G, the eccentricity ec（v） of a vertex v in G is the distance from v to a vertex farthest from v, and d（v） denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξC（G）, is defined as ∑vЕV（G） d（v）ec（v）. In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges（n ≤ m ≤ n ＋ 4）, and propose a conjecture on the graphs with maximal eccentric connectivity index and m edges （m ≥ n ＋ 5）. among the connected graphs with n vertices
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.
文摘The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentricity have a wide range of applications in structure-activity relationships and pharmaceutical drug design etc. In this paper, we investigate the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene. We find a relation between the radius and the number of spokes of a (3, 6)-fullerene. Based on the relation, we give the computing formulas of the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene, respectively.
