On generalized 3-connectivity of the strong product of graphs
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Published:2018
Issue:2
Volume:12
Page:297-317
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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
Author:
Abajo Encarnación1,
Casablanca Rocío1,
Diánez Ana1,
García-Vázquez Pedro1
Abstract
Let G be a connected graph with n vertices and let k be an integer such that
2 ? k ? n. The generalized connectivity kk(G) of G is the greatest positive
integer l for which G contains at least l internally disjoint trees
connecting S for any set S ? V (G) of k vertices. We focus on the
generalized connectivity of the strong product G1 _ G2 of connected graphs
G1 and G2 with at least three vertices and girth at least five, and we prove
the sharp bound k3(G1 _ G2) ? k3(G1)_3(G2) + k3(G1) + k3(G2)-1.
Publisher
National Library of Serbia
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis