Edge-pancyclicity of pancake graph

ABSTRACT

Pancylicity was introduced by Bondy in 1971. A graph G with vertex set $V\left(G\right)$ and edge set $E\left(G\right)$ is pancyclic if it contains cycles of lengths l, for $3\le l\le |V\left(G\right)|$. This concept has been extended to edge-pancyclicity. If every edge of G is in a cycle of every length, G is edge-pancyclic. If every edge lies on cycles of all lengths ranging from k to $|V\left(G\right)|$, G is k-edge-pancyclic. In this paper, we prove that the n-dimensional pancake graph is 7-edge-pancyclic.

KEYWORDS:

• Pancake graph
• edge-pancylicity
• interconnection network
• cycle embedding
• Cayley graph

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 68R10

Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments and suggestions, which improve the presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.