The Kemeny’s Constant and Spanning Trees of Hexagonal Ring Network
Shahid Zaman, Ali N. A. Koam, Ali Al Khabyah, Ali Ahmad
Abstract
Spanning tree () has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers. In the field of medicines, it is helpful to recognize the epidemiology of hepatitis C virus (HCV) infection. On the other hand, Kemeny’s constant () is a beneficial quantifier characterizing the universal average activities of a Markov chain. This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state . Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues. Motivated by Levene and Loizou, we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial. Based on the achieved results, entirely results are obtained for the Möbius hexagonal ring network.