Some Results of Resistance Distance and Kirchhoff Index Based on R-Graph
نویسنده
چکیده
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 Kf(G) is the sum of resistance distances between all pairs of vertices in G. For a graph G, let R(G) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge. Let G1 ⊙ G2, G1 ⊖ G2 be the Rvertex corona and R-edge corona of G1 and G2. In this paper, formulate for the resistance distance and the Kirchhoff index in G1 ⊙ G2 and G1 ⊖ G2 whenever G1 and G2 are arbitrary graphs are obtained. This improves and extends some earlier results.
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