Resistance Distance in the Double Corona Based on R-Graph

• Main Authors: Li Zhang, Jing Zhao, Jia-Bao Liu, Salama Nagy Daoud
• Format: Article
• Language: English
• Published: MDPI AG 2019-01-01
• Series: Mathematics
• Subjects: graph; double corona; resistance distance; inverse
• Online Access: http://www.mdpi.com/2227-7390/7/1/92

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.