A proper total coloring distinguishing adjacent vertices by sums of some product graphs release_eu325h7l6ze5hjvefxmycjqm5e

by Hana Choi, Dongseok Kim, Sungjin Lee, Yeonhee Lee

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2014  

Abstract

In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak PW first introduced this coloring and made a conjecture that the minimal number of colors need to have a proper total coloring distinguishes adjacent vertices by sums is less than or equal to the maximum degree plus 3. We study proper total colorings distinguishing adjacent vertices by sums of some graphs and their products. We find that these graphs satisfy the conjecture.
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Stage   accepted
Date   2014-12-08
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Language   en ?
arXiv  1402.0615v2
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