Algorithm on the Optimal Vertex-Distinguishing Total Coloring of mC9

HE Yu-ping, CHEN Xiang'en

doi:10.13371/j.cnki.chin.q.j.m.2019.03.003

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 3: 242 - 258

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.03.003

Algorithm on the Optimal Vertex-Distinguishing Total Coloring of mC9

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College of Mathematics and Statistics, Northwest Normal University

CHEN Xiang-en(1965-), male, native of Tianshui, Gansu, a professor of Northwest Normal University, M.S.D., engages in graph theory with applications; HE Yu-ping(1990-), female, native of Lanzhou,Gansu, a master of Northwest Normal University, M.S.D., engages in graph theory with applications.

Received date: 2017-11-15

Online published: 2020-08-23

Supported by

Supported by the NNSF of China(Grant No.11761064,61163037)

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Abstract

Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to be the color set of vertex u under f. If Cf(u) = Cf(v)for any two distinct vertices u and v of G, then f is called vertex-distinguishing total coloring of G(in brief VDTC), a vertex distinguishing total coloring using k colors is called k-vertexdistinguishing total coloring of G(in brief k-VDTC). The minimum number k for which there exists a k-vertex-distinguishing total coloring of G is called the vertex-distinguishing total chromatic number of G, denoted by χvt(G). By the method of prior distributing the color sets, we obtain vertex-distinguishing total chromatic number of m C9 in this paper.

Key words： the union of graphs; proper total coloring; vertex-distinguishing total coloring; vertex-distinguishing total chromatic number

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HE Yu-ping, CHEN Xiang'en . Algorithm on the Optimal Vertex-Distinguishing Total Coloring of mC9[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(3) : 242 -258 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.003

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