On Coloring of graph fractional powers

2008/12/08 by Moharram N. Iradmusa, Iradmusa, Moharram N.
Mathematics · #05Cxx #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05Cxx

paper · pdf · doi:10.48550/arxiv.0812.1542

10 pages

arxiv created 2009/02/13 · arxiv updated 2009/12/01

Abstract

\noindent Let G be a simple graph. For any k∈ N, the k-power of G is a simple graph G^k with vertex set V(G) and edge set \xy:d_G(x,y)≤ k\ and the k-subdivision of G is a simple graph G^(1)/(k), which is constructed by replacing each edge of G with a path of length k. So we can introduce the m-power of the n-subdivision of G, as a fractional power of G, that is denoted by G^(m)/(n). In other words G^(m)/(n):=(G^(1)/(n))^m. \noindent In this paper some results about the coloring of G^(m)/(n) are presented when G is a simple and connected graph and (m)/(n)<1.

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