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

Hana Choi, Dongseok Kim, Sungjin Lee, Yeonhee Lee
2015 Communications of the Korean Mathematical Society  
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
more » ... tinguishing adjacent vertices by sums of some graphs and their products. We find that these graphs satisfy the conjecture.
doi:10.4134/ckms.2015.30.1.045 fatcat:5gos3fpfffemxos44xeiutifvm