On Signed Coloring of Signed Graphs

Abstract

The chromatic number of a signed graph is the number of minimum colors required to color a signed graph such that no two adjacent vertices connected by positive edge receives the same color and two vertices connected by negative edge receives opposite color .In this paper we are finding the positive chromatic number for several graph classes. We define a mapping β+:V(G^*)→{+1,+2,....,+k},where G^* is the signed graph of the underlying graph G. The positive chromatic number is the least positive integer k such that k ∈ {+1,+2,...,+k} which holds the conditions for coloring. We use χ_+ to denote positive chromatic number and χ_0 for zero-free chromatic number