The (normalized) Laplacian spectrum and related indexes of generalized quadrilateral graphs
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).
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.
Cite this article
Q. Ma, H. Wang, The (normalized) Laplacian spectrum and related indexes of generalized quadrilateral graphs, J. Math. Comput. Sci. 11 (2021), 1108–1123. https://doi.org/10.28919/jmcs/5253
BibTeX
@article{Ma2021,
author = {Ma, Qi and Wang, Huaping},
title = {The (normalized) Laplacian spectrum and related indexes of generalized quadrilateral graphs},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {1108--1123},
doi = {10.28919/jmcs/5253}
}