Work

Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graphs

Year: 2018

Type: article

Abstract: The status of a vertex u, denoted by σG(u), is the sum of the distances between u and all other vertices in a graph G. The first and second status connectivity indices of a graph G are defined as S1(G)=∑uv∈E(G)[σG(u)+σG(v)] and S2(G)=∑uv∈E(G)σG(u)σG(v) respectively, where E(G) denotes the edge set of G. In this paper we have defined the first and second status co-indices of a graph G as S1¯(G)=∑uv∉E(G)[σG(u)+σG(v)] and S2¯(G)=∑uv∉E(G)σG(u)σG(v) respectively. Relations between status connectivity indices and status co-indices are established. Also these indices are computed for intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus.

Source: AKCE International Journal of Graphs and Combinatorics

DOI: 10.1016/j.akcej.2018.09.002

Authors: Harishchandra S. Ramane, Ashwini S. Yalnaik, Reza Sharafdini

Institutions: Karnatak University, Persian Gulf University

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,226

Funder: University Grants Commission