Laplacian spectra for categorical product networks and its applications

Shin Min Kang, Muhammad Kamran Siddiqui, Najma Abdul Rehman, Muhammad Imran, Mehwish Hussain Muhammad

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.

Original languageEnglish
Article number206
JournalSymmetry
Volume10
Issue number6
DOIs
Publication statusPublished - Jun 1 2018

Keywords

  • Categorical product
  • Global mean-first passage time
  • Kirchhoff index
  • Laplacian spectra
  • Spanning tree

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

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