Edge-pancyclicity of pancake graph

Abstract

Pancylicity was introduced by Bondy in 1971. A graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of lengths l, for 3 ≤ l ≤ |V(G)|. 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(G)|, G is k-edge-pancyclic. In this paper, we prove that the n-dimensional pancake graph is 7-edge-pancyclic.