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Symmetry 2018, 10(6), 206; https://doi.org/10.3390/sym10060206

Laplacian Spectra for Categorical Product Networks and Its Applications

1
Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea
2
Center for General Education, China Medical University, Taichung 40402, Taiwan
3
Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus 57000, Pakistan
4
Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, United Arab Emirates
5
Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan
6
College of Chemistry and Molecular Engineering, Zhengzhou University, Zhengzhou 450001, China
*
Author to whom correspondence should be addressed.
Received: 26 May 2018 / Revised: 5 June 2018 / Accepted: 6 June 2018 / Published: 7 June 2018
(This article belongs to the Special Issue Symmetry and Complexity)
Full-Text   |   PDF [779 KB, uploaded 8 June 2018]   |  

Abstract

The Kirchhoff index, global mean-first passage time, average path length and number of spanning trees are of great importance in the field of networking. The “Kirchhoff index” is known as a structure descriptor index. The “global mean-first passage time” is known as a measure for nodes that are quickly reachable from the whole network. The “average path length” is a measure of the efficiency of information or mass transport on a network, and the “number of spanning trees” is used to minimize the cost of power networks, wiring connections, etc. In this paper, we have selected a complex network based on a categorical product and have used the spectrum approach to find the Kirchhoff index, global mean-first passage time, average path length and number of spanning trees. We find the expressions for the product and sum of reciprocals of all nonzero eigenvalues of a categorical product network with the help of the eigenvalues of the path and cycles. View Full-Text
Keywords: Laplacian spectra; categorical product; Kirchhoff index; global mean-first passage time; spanning tree Laplacian spectra; categorical product; Kirchhoff index; global mean-first passage time; spanning tree
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Kang, S.M.; Siddiqui, M.K.; Rehman, N.A.; Imran, M.; Muhammad, M.H. Laplacian Spectra for Categorical Product Networks and Its Applications. Symmetry 2018, 10, 206.

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