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 S u ) and σ : E ( G ) → { 1 , − 1 } . A signed graph is said to be simple if S u 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.