Affiliation:
1. College of Mathematics and Statistics, Fujian Normal University, Fuzhou, Fujian 350117, P. R. China
2. Center for Applied Mathematics of Fujian Province (Fujian Normal University), Fuzhou, Fujian 350117, P. R. China
Abstract
The cyclic vertex (resp., edge) connectivity of a graph [Formula: see text], denoted by [Formula: see text] (resp., [Formula: see text]), is the minimum number of vertices (resp., edges) whose removal from [Formula: see text] results in a disconnected graph and at least two remaining components contain cycles. Thus, to determine the exact values of [Formula: see text] and [Formula: see text] is important in the reliability assessment of interconnection networks. However, the study of the cyclic vertex (edge) connectivity is less involved. In this paper, we determine the cyclic vertex (edge) connectivity of the burnt pancake graphs [Formula: see text] which is the Cayley graph of the group of signed permutations using prefix reversals as generators. By exploring the combinatorial properties and fault-tolerance of [Formula: see text], we show [Formula: see text] and [Formula: see text] for [Formula: see text]. Moreover, we determine that [Formula: see text] for [Formula: see text].
Funder
National Natural Science Foundation of China
Natural Science Foundation of Fujian Province
Publisher
World Scientific Pub Co Pte Ltd
Subject
Hardware and Architecture,Theoretical Computer Science,Software