Resistance distances in corona and neighborhood corona graphs with Laplacian generalized inverse approach
نویسندگان
چکیده
Let G1 and G2 be two graphs on disjoint sets of n1 and n2 vertices, respectively. The corona of graphs G1 and G2, denoted by G1 ◦ G2, is the graph formed from one copy of G1 and n1 copies of G2 where the i-th vertex of G1 is adjacent to every vertex in the i-th copy of G2. The neighborhood corona of G1 and G2, denoted by G1 ⋄ G2, is the graph obtained by taking one copy of G1 and n1 copies of G2 and joining every neighbor of the i-th vertex of G1 to every vertex in the i-th copy of G2 by a new edge. In this paper, the Laplacian generalized inverse for the graphs G1 ◦G2 and G1 ⋄G2 are investigated, based on which the resistance distances of any two vertices in G1 ◦G2 and G1 ⋄G2 can be obtained. Moreover, some examples as applications are presented, which illustrate the correction and efficiency of the proposed method.
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