Next Article in Journal
A New Family of Chaotic Systems with Different Closed Curve Equilibrium
Next Article in Special Issue
Improved Convergence Analysis of Gauss-Newton-Secant Method for Solving Nonlinear Least Squares Problems
Previous Article in Journal
q-Rung Orthopair Fuzzy Competition Graphs with Application in the Soil Ecosystem
Previous Article in Special Issue
Extending the Applicability of Two-Step Solvers for Solving Equations

## Volume 7, Issue 1 Metrics 0

## Export Article

Open AccessArticle
Mathematics 2019, 7(1), 92; https://doi.org/10.3390/math7010092

# Resistance Distance in the Double Corona Based on R-Graph

1
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
2
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia
3
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin EI Kom 32511, Egypt
*
Author to whom correspondence should be addressed.
Received: 19 December 2018 / Revised: 13 January 2019 / Accepted: 14 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
|   PDF [246 KB, uploaded 17 January 2019]   |

# Abstract

Let $G 0$ be a connected graph on n vertices and m edges. The R-graph $R ( G 0 )$ of $G 0$ is a graph obtained from $G 0$ by adding a new vertex corresponding to each edge of $G 0$ and by joining each new vertex to the end points of the edge corresponding to it. Let $G 1$ and $G 2$ be graphs on $n 1$ and $n 2$ vertices, respectively. The R-graph double corona $G 0 ( R ) ∘ { G 1 , G 2 }$ of $G 0$ , $G 1$ and $G 2$ , is the graph obtained by taking one copy of $R ( G 0 )$ , n copies of $G 1$ and m copies of $G 2$ and then by joining the i-th old-vertex of $R ( G 0 )$ to every vertex of the i-th copy of $G 1$ and the j-th new vertex of $R ( G 0 )$ to every vertex of the j-th copy of $G 2$ . In this paper, we consider resistance distance in $G 0 ( R ) ∘ { G 1 , G 2 }$ . Moreover, we give an example to illustrate the correction and efficiency of the proposed method. View Full-Text
Keywords:
Figures Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0). MDPI and ACS Style

Zhang, L.; Zhao, J.; Liu, J.-B.; Daoud, S.N. Resistance Distance in the Double Corona Based on R-Graph. Mathematics 2019, 7, 92.

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

1