Bipancyclic Properties of Faulty Hypercubes. (14th October 2012)

• Record Type: Journal Article
• Authors: Hung, Chun-Nan; Hsiao, Min-Kun
• Other Names: Ji L. Academic Editor.; Vaccaro U. Academic Editor.; Wallis W. Academic Editor.; Yong X. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2012(2012)
• Publication Date: 2012-10-14
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2012/308595
• Languages: English
• ISSNs: 2090-7788

Abstract

Abstract : 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 Q n denote the n -dimensional hypercube. Let F be a subset of V ( Q n ) ∪ E ( Q n ) such that F can be decomposed into two parts F a v and F e, where F a v is a union of f a v disjoint adjacent pairs of V ( Q n ), and F e consists of f e edges. We prove that Q n - F is bipancyclic if f a v + f e ≤ n - 2 . Moreover, Q n - F is edge bipancyclic if f a v + f e ≤ n - 2 with f a v < n - 2 .