Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A PROPER TOTAL COLORING DISTINGUISHING ADJACENT VERTICES BY SUMS OF SOME PRODUCT GRAPHS

  • Choi, Hana (Department of Mathematics Sungkyunkwan University) ;
  • Kim, Dongseok (Department of Mathematics Kyonggi University) ;
  • Lee, Sungjin (Department of Mathematics Yonsei University) ;
  • Lee, Yeonhee (Department of Mathematics Kyonggi University)
  • Received : 2014.05.02
  • Published : 2015.01.31
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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.

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Acknowledgement

Supported by : Korea Foundation for the Advancement of Science & Creativity (KOFAC)

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