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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 I(G) be the set of newly added vertices. The R-vertex corona of G1 and G2, denoted by G1⊙G2, is the graph obtained from vertex disjoint R(G1) and |V(G1)| copies of G2 by joining the ith vertex of V(G1) to every vertex in the...
In this paper, the generalized inverse representations for the Laplacian block matrices of graphs G1⊡G2 and G1⊟G2 are proposed, based on which the explicit resistance distance can be obtained for the arbitrary two-vertex resistance in the electrical networks. Moreover, some numerical examples are presented, which show the correction and efficiency of the obtained results.
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