Resistance Distances and Kirchhoff Index in Generalised Join Graphs
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Haiyan Chen
Abstract
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 with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G=H[G1, G2, …, Gk ] be the generalised join graph of G1, G2, …, Gk determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of
Acknowledgments
This work is supported by the National Natural Science Foundation of China (grants 11571139, 11301217) and the Natural Science Foundation of Fujian Province, China (grants 2015J01017, 2013J01014).
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Artikel in diesem Heft
- Frontmatter
- Hydrogen and Carbon Vapour Pressure Isotope Effects in Liquid Fluoroform Studied by Density Functional Theory
- Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems
- Resistance Distances and Kirchhoff Index in Generalised Join Graphs
- Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation
- Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux
- Reconstruction of f(T) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies
- Peristaltic Flow of Rabinowitsch Fluid in a Curved Channel: Mathematical Analysis Revisited
- Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium
- Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation
- Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations
- Discrete and Semidiscrete Models for AKNS Equation
Artikel in diesem Heft
- Frontmatter
- Hydrogen and Carbon Vapour Pressure Isotope Effects in Liquid Fluoroform Studied by Density Functional Theory
- Analytic Approximations to Nonlinear Boundary Value Problems Modeling Beam-Type Nano-Electromechanical Systems
- Resistance Distances and Kirchhoff Index in Generalised Join Graphs
- Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation
- Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux
- Reconstruction of f(T) Gravity with Interacting Variable-Generalised Chaplygin Gas and the Thermodynamics with Corrected Entropies
- Peristaltic Flow of Rabinowitsch Fluid in a Curved Channel: Mathematical Analysis Revisited
- Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium
- Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation
- Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations
- Discrete and Semidiscrete Models for AKNS Equation
