On Cayley sum signed graphs-I

Abstract

The Cayley sum graph is a graph whose vertex comprises elements of an abelian group G, and edges are the sum of these vertices belonging to a subset of G, namely, S. We introduce the Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to S. Otherwise, it receives a negative sign. We discuss the properties of the Cayley sum signed graph.