The adjacent vertex distinguishing total coloring of planar graphs

Weifan Wang () and Danjun Huang
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Weifan Wang: Zhejiang Normal University
Danjun Huang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 2, No 13, 379-396

Abstract: Abstract An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices have distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing total coloring of G is denoted by $\chi''_{a}(G)$ . In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of planar graphs G with large maximum degree Δ by showing that if Δ≥14, then $\varDelta+1\leq \chi''_{a}(G)\leq \varDelta+2$ , and $\chi''_{a}(G)=\varDelta+2$ if and only if G contains two adjacent vertices of maximum degree.

Keywords: Adjacent vertex distinguishing total coloring; Planar graph; Maximum degree (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s10878-012-9527-2

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