Decompositions of complete graphs into isomorphic bipartite subgraphs |
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Authors: | R Balakrishnan R Sampath Kumar |
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Institution: | (1) Department of Mathematics, Annamalai University, 608 002 Annamalainagar, India |
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Abstract: | Let |E(G)|= andf, a 1-1 mapping ofV(G) into {0,1,...,}. Thenf is called a -valuation ofG if the induced function given by
, for alluvE(G) is 1-1. A -valuationf is called an -valuation ofG if there exists a nonnegative number such that for everyuvE(G) withf(u)<f(v),f(u)<f(v). Let
denote the graph of then-dimensionalG-cube. ForG=K
3, 3,K
4, 4, andP
k
,it is shown that for any positive integern, then-dimensionalG-cube has an -valuation. This gives rise to decompositions of some complete graphs into certain bipartite graphs. |
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Keywords: | |
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