Further results on independence in direct-product graphs

Jha, P. K. (2000) Further results on independence in direct-product graphs. Ars Combinatoria, 56. pp. 15-24. ISSN 0381-7032

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Abstract

For a graph G, let alpha(G) and tau(G) denote the independence number of G and the matching number of G, respectively. Further, let G x H denote the direct product (also known as Kronecker product, cardinal product, tensor product., categorical product and graph conjunction) of graphs G and H. It is known that alpha(G x H) greater than or equal to max{alpha(G) . \H\, alpha(H) . \G\} =: alpha(G x H) and that tau(G x H) greater than or equal to 2 . tau(G) . tau(H) =: tau(G X H). It is shown that an equality/inequality between ct and ct is independent of an equality/inequality between tau and tau. Further, several results are presented on the existence of a complete matching in each of the two connected components of the direct product of two bipartite graphs. Additional results include an upper bound on alpha(G x H) that is achievable in certain cases.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Information Science and Technology (FIST)
Depositing User: Ms Rosnani Abd Wahab
Date Deposited: 09 Sep 2011 02:42
Last Modified: 11 Nov 2013 04:24
URI: http://shdl.mmu.edu.my/id/eprint/2710

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