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Adjacent vertex distinguishing total colorings of outerplanar graphs. (English) Zbl 1216.05039
Summary: An adjacent vertex distinguishing total coloring of a graph \(G\) is a proper total coloring of \(G\) such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing total coloring of \(G\) is denoted by \(\chi ^{\prime\prime}_{a }(G)\). In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of outerplanar graphs.

MSC:
05C15 Coloring of graphs and hypergraphs
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[1] Appel K, Haken W (1976) Every planar graph map is four colorable. Bull Am Math Soc 82:711–712 · Zbl 0331.05106 · doi:10.1090/S0002-9904-1976-14122-5
[2] Behzad M (1965) Graphs and their chromatic numbers. Doctoral thesis, Michigan State University
[3] Chen X (2007) On the adjacent vertex distinguishing total coloring numbers of graphs with \(\Delta\)=3. Discrete Math. doi: 10.1016/j.disc.2007.07.091
[4] Chen X, Zhang Z (2006) Adjacent-vertex-distinguishing total chromatic number on 2-connected outeplane graph with \(\Delta\)(G). J Lanzhou Univ Nat Sci 42(6):96–102 · Zbl 1120.05305
[5] Fiorini S (1975) On the chromatic index of outerplanar graphs. J Comb Theory Ser B 18:35–38 · Zbl 0288.05105 · doi:10.1016/0095-8956(75)90060-X
[6] Vizing V (1964) On an estimate of the chromatic index of a p-graph. Diskret Anal 3:25–30
[7] Vizing V (1968) Some unsolved problems in graph theory. Usp Mat Nauk 23:117–134 (in Russian) · Zbl 0177.52301
[8] Wang H (2007) On the adjacent vertex distinguishing total chromatic number of the graphs with \(\Delta\)(G)=3. J Comb Optim 14:87–109 · Zbl 1125.05043 · doi:10.1007/s10878-006-9038-0
[9] Wang W, Zhang K (1999) \(\Delta\)-matchings and edge-face chromatic numbers. Acta Math Appl Sin 22:236–242 · Zbl 0959.05096
[10] Zhang S, Chen X, Liu X (2005) Adjacent-vertex-distinguishing total chromatic numbers on 2-connected outer plane graphs with \(\Delta\)(G)=5. Xibei Shifan Daxue Xuebao Ziran Kexue Ban 41(5):8–13 (in Chinese) · Zbl 1092.05504
[11] Zhang Z, Chen X, Li J, Yao B, Lu X, Wang J (2005) On adjacent-vertex-distinguishing total coloring of graphs. Sci China Ser A 48:289–299 · Zbl 1080.05036 · doi:10.1360/03YS0207
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