On cycle graphs

Abstract

The Cycle Graph [Formula: see text] of a graph [Formula: see text] is the edge intersection graph of all induced cycles of [Formula: see text]. In this paper, necessary and sufficient condition on [Formula: see text] such that [Formula: see text] is a connected graph, a tree, a bipartite graph is obtained. Non-existence of forbidden subgraph characterization for cycle graphs is also discussed. It is proved that the girth of cycle graph is three. The relationship between radius of [Formula: see text] and its [Formula: see text] is studied. Similar results on diameter and domination number of [Formula: see text] and its cycle graph are also obtained.