The (normalized) Laplacian spectrum and related indexes of generalized quadrilateral graphs

Qi Ma, Huaping Wang

Abstract


In this paper, we introduce the generalized quadrilateral graph Q(n)(G), which can be got by replacing each edge of the given graph G with a complete bipartite graph Kn,n. We characterize all the spectrum of the graph Q(n)(G) in terms of the given graph. Then we derive the formula for the multiplicative degree-Kirchhoff index, the Kemeny’s constant and the number of spanning trees of Q(n)(G). Finally, we can obtain more about the iterative graph Qr(n)(G).

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Published: 2021-01-27

How to Cite this Article:

Qi Ma, Huaping Wang, The (normalized) Laplacian spectrum and related indexes of generalized quadrilateral graphs, J. Math. Comput. Sci., 11 (2021), 1108-1123

Copyright © 2021 Qi Ma, Huaping Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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