2-Spanning Cyclability Problems of Some Generalized Petersen Graphs

Abstract

A graph G is called r-spanning cyclable if for every r distinct vertices v1, v2, . . . , vr of G, there exists r cycles C1, C2, . . . , Cr in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci. In this paper, we consider the 2-spanning cyclable problem for the generalized Petersen graph GP (n, k). We solved the problem for k ≤ 4. In addition, we provide an additional observation for general k as well as stating a conjecture.

Keywords

• petersen graph
• spanning cyclable
• 05c38
• 05c45