Contents

Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Vertex-distinguishing I- and VI-total colorings of \( S_m \lor F_n, S_m \lor W_n \) and \( F_n \lor W_n^1 \)

Rong Li1, Xiangen Chen1
1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Abstract

We will discuss the vertex-distinguishing I-total colorings and vertex-distinguishing VI-total colorings of three types of graphs: \( S_m \lor F_n, S_m \lor W_n \) and \( F_n \lor W_n \) in this paper. The optimal vertex-distinguishing I (resp. VI)-total colorings of these join graphs are given by the method of constructing colorings according to their structural properties and the vertex-distinguishing I (resp. VI)-total chromatic numbers of them are determined.

Keywords: graph, the join of graphs, I-total coloring, vertex-distinguishing I-total coloring, vertex-distinguishing I-total chromatic number.
Citation
Rong Li, Xiangen Chen. Vertex-distinguishing I- and VI-total colorings of \( S_m \lor F_n, S_m \lor W_n \) and \( F_n \lor W_n^1 \)[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 113. 65-78. .