Comparison Between Second Zagreb Eccentricity Index and Eccentric Connectivity Index of Graphs
Journal Title: Current Trends in Computer Sciences & Applications - Year 2018, Vol 1, Issue 1
Abstract
Throughout this paper we only consider the finite, undirected, simple and connected graphs. The degree of v ∊ V(G), denoted by degG(v), is the number of vertices in G adjacent to v. For any two vertices u; v in a graph G, the distance between them, denoted by (,) G d uv is the length of a shortest path connecting them in G. As usual, let Sn, Pn, Cn, Kn be the star graph, path graph, cycle graph and complete graph, respectively, on n vertices. Other undefined notations and terminology on the graph theory can be found in [1]. For any vertex of graph G, the eccentricity ( ) G ε v (or ε ( ) v for short) is the maximum distance from v to other vertices of G, i.e., ( ) G ε v = maxu≠v (,) G d uv . The eccentricity of a vertex is an important parameter in pure graph theory. The radius of a graph G is denoted by r(G) and defined by r = r(G) = {minε ( ) v | v ∈ V(G)}. Also, the diameter of G, denoted by d(G), is the maximum distance between vertices of a graph G and hence d = d(G) = max{ ε ( ) v | v ∈ V(G)}. A vertex v with ( ) G ε v = r(G) is called a central vertex in G. A graph G with d(G) = r(G) is called a self-centered graph. A graph which contains only two non-central vertices is called almost self-centered graph [2] (ASC graph for short). Moreover, the eccentricity is also applied in chemical graph theory.
Authors and Affiliations
Huimin Li, Fang Gao, Kexiang Xu
Keywords
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