Laplacian Spectra for Categorical Product Networks and Its Applications

• Main Authors: Shin Min Kang, Muhammad Kamran Siddiqui, Najma Abdul Rehman, Muhammad Imran, Mehwish Hussain Muhammad
• Format: Article
• Language: English
• Published: MDPI AG 2018-06-01
• Series: Symmetry
• Subjects: Laplacian spectra; categorical product; Kirchhoff index; global mean-first passage time; spanning tree
• Online Access: http://www.mdpi.com/2073-8994/10/6/206

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.