Characterization of 2-Path Product Signed Graphs with Its Properties

Abstract

A signed graph is a simple graph where each edge receives a sign positive or negative. Such graphs are mainly used in social sciences where individuals represent vertices friendly relation between them as a positive edge and enmity as a negative edge. In signed graphs, we define these relationships (edges) as of friendship (“+” edge) or hostility (“−” edge). A 2-path product signed graph Strue#^S of a signed graph S is defined as follows: the vertex set is the same as S and two vertices are adjacent if and only if there exists a path of length two between them in S. The sign of an edge is the product of marks of vertices in S where the mark of vertex u in S is the product of signs of all edges incident to the vertex. In this paper, we give a characterization of 2-path product signed graphs. Also, some other properties such as sign-compatibility and canonically-sign-compatibility of 2-path product signed graphs are discussed along with isomorphism and switching equivalence of this signed graph with 2-path signed graph.

Characterization of 2-Path Signed Network

“…Signed networks of some intersection networks have been already studied [30][31][32][33]. Also path graphs of signed graphs are discussed in [34][35][36][37][38]. In this paper, we try and establish the results for signed networks defined on 2-path networks.…”