Resistance Distance in the Double Corona Based on R -Graph

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.