Further results on independence in direct-product graphs
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...
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| Format: | Article |
| Language: | English |
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Charles Babbage Res Ctr
2000
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| Online Access: | http://shdl.mmu.edu.my/2710/ http://shdl.mmu.edu.my/2710/1/Further%20results%20on%20independence%20in%20direct-product%20graphs.pdf |
| Summary: | 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. |
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