One conjecture of bubble-sort graphs

Authors:
Hai-zhong Shi;Pan-feng Niu;Jian-bo Lu
Affiliations:
College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730030, Gansu, Peoples Republic of China;College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730030, Gansu, Peoples Republic of China;College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730030, Gansu, Peoples Republic of China
Venue:
Information Processing Letters
Year:
2011

Citing 6
Cited 0

A Group-Theoretic Model for Symmetric Interconnection Networks

IEEE Transactions on Computers
Graph Theory With Applications

Graph Theory With Applications
Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs

Information Processing Letters
Hamiltonian laceability of bubble-sort graphs with edge faults

Information Sciences: an International Journal
Graph Theory

Graph Theory
Hamiltonian Decomposition of Some Interconnection Networks

COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications

Quantified Score

Hi-index	0.89

Visualization

Abstract

The bubble-sort graph is an important interconnection network designed from Cayley graph model. One conjecture is proposed in Shi and Lu (2008) [10] as follows: for any integer n=2, if n is odd then bubble-sort graph B"n is a union of n-12 edge-disjoint hamiltonian cycles; if n is even then bubble-sort graph B"n is a union of n-22 edge-disjoint hamiltonian cycles and its perfect matching that has no edges in common with the hamiltonian cycles. In this paper, we prove that conjecture is true for n=5,6.