The generalized 3-connectivity of star graphs and bubble-sort graphs

Shasha Li, Jianhua Tu and Chenyan Yu

Applied Mathematics and Computation, 2016, vol. 274, issue C, 41-46

Abstract: For S ⊆ G, let κ(S) denote the maximum number r of edge-disjoint trees T1,T2,…,Tr in G such that V(Ti)∩V(Tj)=S for any i,j∈{1,2,⋯,r} and i ≠ j. For every 2 ≤ k ≤ n, the generalized k-connectivity of G κk(G) is defined as the minimum κ(S) over all k-subsets S of vertices, i.e., κk(G)= min {κ(S)|S⊆V(G)and|S|=k}. Clearly, κ2(G) corresponds to the traditional connectivity of G. The generalized k-connectivity can serve for measuring the capability of a network G to connect any k vertices in G. Cayley graphs have been used extensively to design interconnection networks. In this paper, we restrict our attention to two classes of Cayley graphs, the star graphs Sn and the bubble-sort graphs Bn, and investigate the generalized 3-connectivity of Sn and Bn. We show that κ3(Sn)=n−2 and κ3(Bn)=n−2.

Keywords: Generalized 3-connectivity; Internally disjoint trees; Cayley graphs; Star graphs; Bubble-sort graphs (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:274:y:2016:i:c:p:41-46

DOI: 10.1016/j.amc.2015.11.016

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