Common-Edge Sigraphs
Mukti Acharya, Deepa Sinha, S. Arumugam · AKCE International Journal of Graphs and Combinatorics · 2006
A signed graph (or, sigraph in short) is a graph G in which each edge x carries a value s(x) 2 { 1,+1} called its sign. Given a sigraph S, a new sigraph CE(S), called the common-edge sigraph of S, is that sigraph whose vertex-set is the set of pairs of adjacent edges in S and two vertices of CE(S) are adjacent if the pairs of adjacent edges of S have exactly one edge in common, with the same sign as that of the common edge. In this paper, we study common-edge sigraphs and characterize sigraphs whose common-edge sigraphs and second iterated line sigraphs are switching equivalent. Also, we determine the sigraphs S for which their common-edge sigraphs are balanced, S -consistent and S -cyclecompatible, respectively.