The energy and edge energy of some Cayley graphs on the abelian group $\mathbb{Z}_{n}^{4}$

Document Type : Original paper

Author

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

Abstract

Let $G=(V, E)$ be a simple graph such that $\lambda_1, \ldots, \lambda_n$ be the eigenvalues of $G$. The energy of graph $G$ is denoted by $E(G)$ and is defined as $E(G)=\sum_{i=1}^{n}|\lambda_{i}|$. The edge energy of $G$ is the energy of line graph $G$. In this paper, we investigate the energy and edge energy for two Cayley graphs on the abelian group $\mathbb{Z}_{n}^{4}$, namely, the Sudoku graph and the positional Sudoku graph. Also, we obtain graph energy and edge energy of the complement of these two graphs.

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 1
March 2024
Pages 119-130

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