Neighbor product distinguishing total colorings of corona of subcubic graphs
Abstract
A proper $k$-total coloring $c$ of a graph $G$ is a mapping $c$from $V(G)\bigcup E(G)$ to $[k]=\{1,2,\cdots,k\}$ such that$c(x)\neq c(y)$ where $x$, $y\in V(G)\bigcup E(G)$ and $x$ isadjacent to or incident with $y$. Let $\prod(v)$ denote the product of $c(v)$ and the colors on all the edges incident with $v$. For each edge $uv\in E(G)$, if $\prod(u)\neq \prod(v)$, then the coloring $c$ is called a neighbor product distinguishing total coloring of $G$. By $\chi''_{\prod}(G)$, we denote the minimalvalue of $k$ in such a coloring of $G$. In this paper, we considered the corona graph $G$ of two arbitrary subcubic graphs and confirmed that $\chi''_{\prod}(G)\leq\Delta(G)+3$.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Photochromic and Fluorescence Chemistry
Publication details
- Journal / source
- Hacettepe Journal of Mathematics and Statistics
- Publisher
- Hacettepe University
- Volume
- 55
- Issue
- 4
- Pages
- 1658–1663
- Publication date
- 18 May 2026
- Language
- EN