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

Author:

Cao Jinde1,Liu Jia-Bao21,Wang Shaohui3

Affiliation:

1. School of Mathematics, Southeast University, Nanjing 210096, P. R. China

2. School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China

3. Department of Mathematics, Savannah State University, Savannah, GA 31404, USA

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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