A PROPER TOTAL COLORING DISTINGUISHING ADJACENT VERTICES BY SUMS OF SOME PRODUCT GRAPHS

Title & Authors
A PROPER TOTAL COLORING DISTINGUISHING ADJACENT VERTICES BY SUMS OF SOME PRODUCT GRAPHS
Choi, Hana; Kim, Dongseok; Lee, Sungjin; Lee, Yeonhee;

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 [15] 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 prove that these graphs satisfy the conjecture.
Keywords
coloring;total coloring;proper coloring distinguishing adjacent vertices by sum;
Language
English
Cited by
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