Some resistance distance and distance-based graph invariants and number of spanning trees in the tensor product of P2 and Kn

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0057

Keywords:

Kirchhoff index, Degree-Kirchhoff index, Normalized Laplacian, Spanning tree

Abstract

The resistance distance (Kirchhoff index and multiplicative Kirchhoff index) and distance-based (Wiener index and Gutman index) graph invariants of ?n = P2 ×Kn are considered. Firstly by using the decomposition theorem, we procure the Laplacian and Normalized Laplacian spectrum for graph ?n, respectively. Based on which, we can procured the formulae for the number of spanning trees and some resistance distance and distance-based graph invariants of graph ?n. Also, it is very interesting to see that when n tends to infinity, Kf (?n) is a polynomial and W (?n) is a quadratic polynomial.

Author Biographies

Muhammad Shoaib Sardar, Anhui University.

School of Mathematical Sciences.

Murat Cancan, Van Yüzüncü Yil University.

Faculty of Education.

Süleyman Ediz, Van Yüzüncü Yil University.

Faculty of Education.

Wasim Sajjad, Anhui University.

School of Mathematical Sciences.

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Published

2020-07-28

How to Cite

[1]
M. S. Sardar, M. Cancan, S. Ediz, and W. Sajjad, “Some resistance distance and distance-based graph invariants and number of spanning trees in the tensor product of P2 and Kn”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 919-932, Jul. 2020.

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