Graph Powers and Graph Homomorphisms

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dc.creatorHajiabolhassan, Hossein
dc.creatorTaherkhani, Ali
dc.date2008-08-04
dc.date2008-09-02
dc.date.accessioned2026-07-07T09:59:35Z
dc.date.available2026-07-07T09:59:35Z
dc.descriptionIn this paper we investigate some basic properties of fractional powers. In this regard, we show that for any rational number $1\leq {2r+1\over 2s+1}< og(G)$, $G^{2r+1\over 2s+1}\longrightarrow H$ if and only if $G\longrightarrow H^{-{2s+1\over 2r+1}}.$ Also, for two rational numbers ${2r+1\over 2s+1} < {2p+1\over 2q+1}$ and a non-bipartite graph $G$, we show that $G^{2r+1\over 2s+1} < G^{2p+1\over 2q+1}$. In the sequel, we introduce an equivalent definition for circular chromatic number of graphs in terms of fractional powers. We also present a sufficient condition for equality of chromatic number and circular chromatic number.
dc.identifierhttps://arxiv.org/abs/0808.0362
dc.identifierhttp://arxiv.org/abs/0808.0362
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168073
dc.subjectCombinatorics
dc.titleGraph Powers and Graph Homomorphisms
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