A Note on the Adjacent Vertex Distinguishing Total Chromatic Number of Graph

Zhi Wen Wang

doi:10.4028/www.scientific.net/KEM.474-476.2341

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A Note on the Adjacent Vertex Distinguishing Total Chromatic Number of Graph
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HomeKey Engineering MaterialsKey Engineering Materials Vols. 474-476A Note on the Adjacent Vertex Distinguishing Total...

A Note on the Adjacent Vertex Distinguishing Total Chromatic Number of Graph

Abstract:

A total coloring of a simple graph G is called adjacent vertex distinguishing if for any two adjacent and distinct vertices u and v in G, the set of colors assigned to the vertices and the edges incident to u differs from the set of colors assigned to the vertices and the edges incident to v. In this paper we shall prove the series-parallel graph with maximum degree 3 and the series-parallel graph whose the number of edges is the double of maximum degree minus 1 satisfy the adjacent vertex distinguishing total coloring conjecture.

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Key Engineering Materials (Volumes 474-476)

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2341-2345

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.474-476.2341

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Online since:

April 2011

Authors:

Zhi Wen Wang

Keywords:

Adjacent Vertex Distinguishing Total Coloring, Series-Parallel Graph

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