Mathematics

CLC number: O157.5

I-Total Coloring and VI-Total Coloring of mC₄ Vertex-Distinguished by Multiple Sets

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

^† To whom correspondence should be addressed. E-mail: chenxe@nwnu.edu.cn

Received: 8 December 2022

Abstract

We give the optimal I-(VI-)total colorings of $m{C}_{\mathrm{4}}$ which are vertex­distinguished by multiple sets by the use of the method of constructing a matrix whose entries are the suitable multiple sets or empty sets and the method of distributing color set in advance. Thereby we obtain I-(VI-)total chromatic numbers of $m{C}_{\mathrm{4}}$ which are vertex-distinguished by multiple sets.