0n removable cycles in graphs and digraphs

Document Type: Research articles

Author

Department of Mathematics University of thi-qar collage of education for pure sciences

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.

Keywords