mK的点可区别全染色mK的点可区别全染色

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J4 ›› 2012, Vol. 50 ›› Issue (4): 686-692.

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Vertex-Distinguishing Total Colorings-of-mK4

CHEN Xiangen¹, WANG Zhiwen², MA Yanrong¹, YAO Bing¹

1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China;
2. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China

Received:2011-09-22 Online:2012-07-01 Published:2012-09-07
Contact: CHEN Xiangen1 E-mail:chenxe@nwnu.edu.cn

Abstract

Abstract:

The problem of vertex-distinguishing total colorings of graphs was discussed via the methods of distributing color sets in advance, constructing concrete coloring with the help of matrices and recurrence method. The exact value of the vertex-distinguishing total chromatic number χvt(mK4) of the union mK4 of m vertex-disjoint K4 was given, that is “If k-14<4m≤k4, m≥2, k≥6, then χvt(mK4)=k”. This illustrates that the VDTC conjecture is valid for mK4.

Key words: graphs, vertexdistinguishing total coloring, vertexdistinguishing total chromatic number

CLC Number:

CHEN Xiangen, WANG Zhiwen, MA Yanrong, YAO Bing. Vertex-Distinguishing Total Colorings-of-mK4[J].J4, 2012, 50(4): 686-692.

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Vertex-Distinguishing Total Colorings-of-mK4

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