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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)
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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: graph; double corona; resistance distance; inverse graph; double corona; resistance distance; inverse
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Zhang, L.; Zhao, J.; Liu, J.-B.; Daoud, S.N. Resistance Distance in the Double Corona Based on R-Graph. Mathematics 2019, 7, 92.

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