Domination Number in Graphs with Minimum Degree Two-中国期刊网

摘要 AsetDofverticesofagraphG=(V,E)iscalledadominatingsetifeveryvertexofVnotinDisadjacenttoavertexofD.In1996,Reedprovedthateverygraphofordernwithminimumdegreeatleast3hasadominatingsetofcardinalityatmost3n/8.InthispaperwegeneralizeReed'sresult.WeshowthateverygraphGofordernwithminimumdegreeatleast2hasadominatingsetofcardinalityatmost(3n+|V_2|)/8,whereV_2denotesthesetofverticesofdegree2inG.Asanapplicationoftheaboveresult,weshowthatfork>1,thek-restricteddominationnumberr_k(G,y)<(3n+5k)/8forallgraphsofordernwithminimumdegreeatleast3.

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Domination Number in Graphs with Minimum Degree Two

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Domination Number in Graphs with Minimum Degree Two

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