Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901439 | Applied Mathematics and Computation | 2018 | 10 Pages |
Abstract
Given a graph G and a non-negative integer h, the h-extra connectivity (or h-extra edge-connectivity, resp.) of G, denoted by κh(G) (or λh(G), resp.), is the minimum cardinality of a set of vertices (or edges, resp.) in G, if it exists, whose deletion disconnects G and leaves each remaining component with more than h vertices. In this paper, we obtain a tight upper bound of the h-extra connectivity and the h-extra edge-connectivity of n-dimensional balanced hypercubes BHn for nâ¯â¥â¯2 and hâ¤2nâ1. As an application, we prove that κ4(BHn)=κ5(BHn)=6nâ8 and λ3(BHn)=8nâ8, which improves the previously known results given by Yang (2012) and Lü (2017).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Da-Wei Yang, Yan-Quan Feng, Jaeun Lee, Jin-Xin Zhou,