The resistance distance and Kirchhoff index on quadrilateral graph and pentagonal graph
Combinatorics
2018-12-11 v1 Spectral Theory
Abstract
The quadrilateral graph Q(G) is obtained from G by replacing each edge in G with two parallel paths of length 1 and 3, whereas the pentagonal graph W(G) is obtained from G by replacing each edge in G with two parallel paths of length 1 and 4. In this paper, closed-form formulas of resistance distance and Kirchhoff index for quadrilateral graph and pentagonal graph are obtained whenever G is an arbitrary graph.
Keywords
Cite
@article{arxiv.1812.02304,
title = {The resistance distance and Kirchhoff index on quadrilateral graph and pentagonal graph},
author = {Qun Liu and Zhongzhi Zhang},
journal= {arXiv preprint arXiv:1812.02304},
year = {2018}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1810.03327