On Coloring of graph fractional powers

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dc.creatorIradmusa, Moharram N.
dc.date2008-12-08
dc.date2009-02-13
dc.date.accessioned2026-07-07T12:40:50Z
dc.date.available2026-07-07T12:40:50Z
dc.description\noindent Let $G$ be a simple graph. For any $k\in N$, the $k-$power of $G$ is a simple graph $G^k$ with vertex set $V(G)$ and edge set $\{xy:d_G(x,y)\leq k\}$ and the $k-$subdivision of $G$ is a simple graph $G^{\frac{1}{k}}$, 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 $G^{\frac{m}{n}}$. In other words $G^{\frac{m}{n}}:=(G^{\frac{1}{n}})^m$. \noindent In this paper some results about the coloring of $G^{\frac{m}{n}}$ are presented when $G$ is a simple and connected graph and $\frac{m}{n}<1$.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0812.1542
dc.identifierhttp://arxiv.org/abs/0812.1542
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219569
dc.subjectCombinatorics
dc.subject05Cxx
dc.titleOn Coloring of graph fractional powers
dc.typetext

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