Bipancyclic Properties of Faulty Hypercubes

Abstract EN

A bipartite graph G=(V,E) is bipancyclic if it contains cycles of every even length from 4 to |V| and edge bipancyclic if every edge lies on a cycle of every even length from 4 to |V|.

Let Qn denote the n-dimensional hypercube.

Let F be a subset of V(Qn)∪E(Qn) such that F can be decomposed into two parts Fav and Fe, where Fav is a union of fav disjoint adjacent pairs of V(Qn), and Fe consists of fe edges.

We prove that Qn-F is bipancyclic if fav+fe≤n-2.

Moreover, Qn-F is edge bipancyclic if fav+fe≤n-2 with fav