k-Cycle resonant graphs Original Research Article

A connected graph G is said to be k-cycle resonant if, for 1 ⩽t⩽k, any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M-alternating cycle. In this paper, we at the first time introduce the concept of k-cycle resonant graphs, and investigate some properties of k-cycle resonant graphs. Some simple necessary and sufficient conditions for a graph to be k-cycle resonant are given. The construction of k-cycle resonant hexagonal systems are also characterized.