On Incidence Graphs

Abstract

An incidence graph of a given graph \(G\), denoted by \(I(G)\), has its own vertex set \(V(I(G)) = \{(ve) | v \in V(G), e \in E(G) \text{ and } v \text{ is incident to } e \text{ in } G\}\) such that the pair \(((ue)(vf))\) of vertices \((ue) (vf) \in V(I(G))\) is an edge of \(I(G)\) if and only if there exists at least one case of \(u = v, e = f, uv = e\) or \(uv = f\). In this paper, we carry out a constructive definition on incidence graphs, and investigate some properties of incidence graphs and some edge-colorings on several classes of them.