Abstract
The resistance distance between any two vertices of a connected graph is defined as the net effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. In this article, using electric network approach and combinatorial approach, we derive exact expression for resistance distances between any two vertices of polyacene graphs.
Highlights
Let G (V(G), E(G)) be a connected graph
It turns out that the resistance distance has some pure mathematical interpretations, which could be expressed in terms of the generalized inverse of the Laplacian matrix [1], the number of spanning trees and spanning bi-trees [2], and random walks on graphs [3, 4]
The computation of resistance distances is a classical problem in electrical circuit theory, which has attracted much attention
Summary
Let G (V(G), E(G)) be a connected graph. It is interesting to consider distance functions on G. Besides being an intrinsic graph metric and an important component of electrical circuit theory, resistance distance turns out to have important applications in chemistry For this reason, resistance distance has been widely studied in the mathematical, chemical, and physical literature. It is interesting to note that a good deal of attention has been paid on resistance distances in plane networks, such as Platonic solids, fullerene graphs, wheels, fans, ladder graphs, Apollonian network, Sierpinski Gasket Network, m × n resistor network, and straight linear 2-tree. Motivated by this fact, we are devoted to considering other interesting plane networks. Using electrical network approach and resistance distance local rules, we derive exact expression for resistance distances between any two vertices of Ln
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