On Pseudo-Balancing of Path-Induced Signed Graphs

Abstract

The path decomposition of a graph G is the partition of its edges into distinct paths. Pendant number of a graph G is the least number of terminal vertices  involved in the path decomposition of G. If the signed function is induced by the terminal vertices of the path-decomposed graph, it is called path-induced signed graph. In this paper, we identify few classes of balanced signed graphs and also introduce and examine a related concept, namely, pseudo-balancing of path-induced signed graphs.

Key words and phrases. Path decomposition, pendant number, signed graphs, path-induced signed graphs, pseudo-balanced path-induced signed graphs.

2010 Mathematics Subject Classification. MSC 05C22; 05C38