Separation of Cartesian products of graphs into several connected components by the removal of edges
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Published:2021
Issue:2
Volume:15
Page:357-377
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ISSN:1452-8630
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Container-title:Applicable Analysis and Discrete Mathematics
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language:en
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Short-container-title:APPL ANAL DISCRETE M
Affiliation:
1. University of Maribor, FME, Maribor, Slovenia
Abstract
Let G = (V (G),E(G)) be a graph. A set S ? E(G) is an edge k-cut in G if the
graph G-S = (V (G), E(G) \ S) has at least k connected components. The
generalized k-edge connectivity of a graph G, denoted as ?k(G), is the
minimum cardinality of an edge k-cut in G. In this article we determine
generalized 3-edge connectivity of Cartesian product of connected graphs G
and H and describe the structure of any minimum edge 3-cut in G2H. The
generalized 3-edge connectivity ?3(G2H) is given in terms of ?3(G) and ?3(H)
and in terms of other invariants of factors G and H.
Publisher
National Library of Serbia
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis