0n removable cycles in graphs and digraphs

Abstract

In this paper we define the removable cycle that, if $Im$ is a

class of graphs, $Gin Im$, the cycle $C$ in $G$ is called

removable if $G-E(C)in Im$. The removable cycles in Eulerian

graphs have been studied. We characterize Eulerian graphs which

contain two edge-disjoint removable cycles, and the necessary and

sufficient conditions for Eulerian graph to have removable cycles

have been introduced. Further, the even and odd removable cycles in

Eulerian graphs have also been studied. The necessary and sufficient

conditions for regular graphs (digraphs) to have a removable cycles

have been characterized. We also define, the removable cycle class.