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The vertex‐face total chromatic number of Halin graphs
Author(s) -
Lam Peter C. B.,
Zhang Zhongfu
Publication year - 1997
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199710)30:3<167::aid-net2>3.0.co;2-j
Subject(s) - combinatorics , vertex (graph theory) , mathematics , chromatic scale , face (sociological concept) , graph , social science , sociology
In this paper, we shall first prove that for a Halin graph G , 4 ≤ χ T ( G ) ≤ 6, where χ T ( G ) is the vertex‐face total chromatic number of G . Second, we shall establish a sufficient condition for a Halin graph to have a vertex‐face total chromatic number of 6. Finally, we shall give a necessary and sufficient condition for a Halin graph to have a vertex‐face total chromatic number of 4 and describe a way of assigning the four colors to such graphs. © 1997 John Wiley & Sons, Inc. Networks 30:167–170, 1997