On the adjacent vertex distinguishing total coloring numbers of graphs with Δ = 3

An adjacent vertex distinguishing total-coloring of a simple graph G is a proper total-coloring of G such that no pair of adjacent vertices meets the same set of colors. The minimum number of colors χ a ″ ( G ) required to give G an adjacent vertex distinguishing total-coloring is studied. We proved...

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Bibliographic Details
Published inDiscrete mathematics Vol. 308; no. 17; pp. 4003 - 4007
Main Author Chen, Xiang’en
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.09.2008
Subjects
Adjacent vertex distinguishing total-coloring
Simple graph
Adjacent vertex distinguishing total-coloring
Simple graph
05C15
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Summary:An adjacent vertex distinguishing total-coloring of a simple graph G is a proper total-coloring of G such that no pair of adjacent vertices meets the same set of colors. The minimum number of colors χ a ″ ( G ) required to give G an adjacent vertex distinguishing total-coloring is studied. We proved χ a ″ ( G ) ⩽ 6 for graphs with maximum degree Δ ( G ) = 3 in this paper.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2007.07.091