Some Results On the Splitting Signed Graphs S(S)

By : Sangita Kansal, Rashmi Jain, Mukti Acharya

Page No: 23-32

Abstract
A signed graph (or, in short, sigraph) S = (Su, s) consists of an underlying graph Su := G = (V, E) and a function s : E(Su) ? {+, -}, called the signature of S. A marking of S is a function m: V(S) ? {+, -}. The canonical marking of a signed graph S, denoted ms, is given as The splitting signed graph of a signed graph S, denoted S(S), is formed as follows: Take a copy of S and for each vertex v of S, take a new vertex v ¢. Join v ¢ to all vertices u Î N(v) by negative edge, if ms(u) = ms(v) = - in S and by positive edge otherwise. Here, N(v) is the set of all adjacent vertices to v. In this paper, we give structural characterization of signed graph S so that S(S) is balanced and ?-consistent. We also establish a characterization of splitting signed graphs S(S).

Authors :
Rashmi Jain and Sangita Kansal : Department of Applied Mathematics Delhi Technological University Shahbad Daulatpur, Main Bawana Road Delhi- 110 042, India.
Mukti Acharya : House No 22, 10th Cross, 5th Main MalleshPalya, Bangaluru-560 075, India.