Properties of topological spaces associated with sigraphs

A signed graph (sigraph) S is an ordered pair (G, σ) where G is a graph called the underlying graph of S (denoted by Su) and σ:E(G)→{1,−1}. A signed graph is said to be simple if Su is simple. Given a simple sigraph, we associate a pair of topologies on the vertex set V(S). In this paper, properties of these topologies are determined interms of the properties of the corresponding sigraph.