Resistance distances in corona and neighborhood corona networks based on Laplacian generalized inverse approach

Abstract

Let [Formula: see text] and [Formula: see text] be two graphs on disjoint sets of [Formula: see text] and [Formula: see text] vertices, respectively. The corona of graphs [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the graph formed from one copy of [Formula: see text] and [Formula: see text] copies of [Formula: see text] where the [Formula: see text]th vertex of [Formula: see text] is adjacent to every vertex in the [Formula: see text]th copy of [Formula: see text]. The neighborhood corona of [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the graph obtained by taking one copy of [Formula: see text] and [Formula: see text] copies of [Formula: see text] and joining every neighbor of the [Formula: see text]th vertex of [Formula: see text] to every vertex in the [Formula: see text]th copy of [Formula: see text] by a new edge. In this paper, the Laplacian generalized inverse for the graphs [Formula: see text] and [Formula: see text] is investigated, based on which the resistance distances of any two vertices in [Formula: see text] and [Formula: see text] can be obtained. Moreover, some examples as applications are presented, which illustrate the correction and efficiency of the proposed method.