Abstract
A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices' coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs P n ∨P n ,Cn∨C n and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs P n ∨P n and Cn∨C n .
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Supported by the Xianyang Normal University Foundation for Basic Research (No.06XSYK266) and Com2MaC-KOSEF( R11-1999-054).
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Wang, Zw., Yan, Lh. & Zhang, Zf. Vertex Distinguishing Equitable Total Chromatic Number of Join Graph. Acta Mathematicae Applicatae Sinica, English Series 23, 433–438 (2007). https://doi.org/10.1007/s10255-007-0383-2
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DOI: https://doi.org/10.1007/s10255-007-0383-2