Vertex-distinguishing IE-total Colorings of Complete Bipartite Graphs K8;n

SHI Jin, CHEN Xiang-en

doi:10.13371/j.cnki.chin.q.j.m.2016.02.005

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 2: 147 - 154

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.02.005

Vertex-distinguishing IE-total Colorings of Complete Bipartite Graphs K_8;n

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College of Mathematics and Statistics,Northwest Normal University

SHI Jin(1990-), female, native of Tianshui, Gansu, a graduate student of Northwest Normal University, engages in graph theory with applications; CHEN Xiang-en(1965-), male, native of Tianshui, Gansu, a professor of Northwest Normal University, M.S.D., engages in graph theory with applications.

Received date: 2014-04-07

Online published: 2020-11-06

Supported by

Supported by the National Natural Science Foundation of China(61163037,61163054,11261046,61363060)；

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Abstract

Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C（x） be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C（u） ≠ C（v） for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_vt^ie（G） and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K_8,nare discussed in this paper. Particularly, the VDIET chromatic number of K_8,nare obtained.

Key words： complete bipartite graphs; IE-total coloring; vertex-distinguishing IE-total coloring; vertex-distinguishing IE-total chromatic number

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SHI Jin, CHEN Xiang-en . Vertex-distinguishing IE-total Colorings of Complete Bipartite Graphs K_8;n[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(2) : 147 -154 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.02.005

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