Laplacian and Wiener index of extension of zero divisor graph. (English) Zbl 07894681
Summary: The main purpose of this paper is to study the Laplacian eigenvalues of the extension of the zero divisor graph, \( \Gamma_e ( \mathbb{Z}_n ) ,\) for some particular values of \(n\). We characterize the values of \(n\) that give the equality of the spectral radius and the second-smallest eigenvalue of \(\Gamma_e ( \mathbb{Z}_n )\). Finding Wiener index of \(\Gamma_e ( \mathbb{Z}_n )\) in terms of its Laplacian eigenvalues is another objective of this paper.
MSC:
05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
05C12 | Distance in graphs |
15A18 | Eigenvalues, singular values, and eigenvectors |
13A70 | General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) |
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