# Resistance distance

@article{Klein1993ResistanceD, title={Resistance distance}, author={Douglas J. Klein and Milan Randic}, journal={Journal of Mathematical Chemistry}, year={1993}, volume={12}, pages={81-95} }

The theory of resistive electrical networks is invoked to develop a novel view: if fixed resistors are assigned to each edge of a connected graph, then the effective resistance between pairs of vertices is a graphical distance. Several theorems concerning this novel distance function are established.

#### 851 Citations

Resistance Distances in Linear Polyacene Graphs

- Frontiers in Physics
- 2020

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… Expand

The Kirchhoff Index of Weighted Graphs 1

- Mathematics
- 2013

The resistance distance between two vertices of a connected graph G is computed as the effective resistance in the corresponding network constructed from G by replacing each edge of G with an unit… Expand

Some Bounds for the Kirchhoff Index of Graphs

- Mathematics
- 2014

The resistance distance between two vertices of a connected graph is defined as the effective resistance between them in the corresponding electrical network constructed from by replacing each edge… Expand

The resistance distances of electrical networks based on Laplacian generalized inverse

- Mathematics, Computer Science
- Neurocomputing
- 2015

In this paper, the generalized inverse representations for the Laplacian block matrices of graphs G 1 ? G 2 and G 1 ?s G 2 are proposed, based on which the explicit resistance distance can be… Expand

Some results on resistance distances and resistance matrices

- Mathematics
- 2015

In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an… Expand

Results on resistance distance and Kirchhoff index of graphs with generalized pockets

- Mathematics
- 2019

In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of graphs with generalized pockets in terms of the resistance distance and Kirchhoff index of the factor… Expand

Some Results of Resistance Distance and Kirchhoff Index Based on R-Graph

- 2016

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge… Expand

Computation of resistance distance and Kirchhoff index of the two classes of silicate networks

- Computer Science, Mathematics
- Appl. Math. Comput.
- 2020

The resistance distance between any two arbitrary vertices of a chain silicates network and a cyclic silicate network was procured by utilizing techniques from the theory of electrical networks, i.e., the series and parallel principles, the principle of elimination, the star-triangle transformation and the delta-wye transformation. Expand

Some Two-Vertex Resistances of Nested Triangle Network

- Computer Science, Mathematics
- Circuits Syst. Signal Process.
- 2021

In this paper, some two-vertex resistances of nested triangle network was procured by utilizing techniques from the theory of electrical networks, i.e., the series and parallel principles, the principle of substitution, the star-triangle transformation and the delta-wye transformation. Expand

A Note On Bipartite Graphs with Domination Number 2 and 3

- European Journal of Science and Technology
- 2021

When each edge of a connected G graph is replaced by a unit resistor, the resistance distance is computed as the effective resistance between any two vertices in G . The Kirchhoff index of G is given… Expand

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