1. Sudoku Number of Corona of Graphs
- Author
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Nair, Manju S, S, Aparna Lakshmanan, and Arumugam, S
- Subjects
Mathematics - Combinatorics ,05C15, 05C76 - Abstract
Let $G = (V,E)$ be a graph of order $n$ with chromatic number $\chi(G) = k$, let $S \subset V$ and let $C_0$ be a $k$-coloring of the induced subgraph $G[S]$. The coloring $C_0$ is called an extendable coloring, if $C_0$ can be extended to a $k$-coloring of $G$ and it is a Sudoku coloring of $G$ if the extension is unique. The smallest order of such an induced subgraph $G[S]$ of $G$ which admits a Sudoku coloring is called the Sudoku number of $G$ and is denoted by $sn(G)$. In this paper, we first introduce the notion of uniquely color extendable vertex and then we obtain the lower and upper bounds for the Sudoku number of $G \circ K_1$. Some families of graphs which attain these bounds are also obtained. The exact value of the Sudoku number of corona of $C_n$, $W_n$ and $K_n$ with $K_1$ and $C_n \circ P_m$ are also obtained.
- Published
- 2024