2015/03/18 by Jia‐Bao Liu, Liu, Jia-Bao, Xiang-Feng Pan +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1503.07842
openalex publication_date 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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\diamond 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\diamond G2 are investigated, based on which the resistance distances of any two vertices in G1∘ G2 and G1\diamond G2 can be obtained. Moreover, some examples as applications are presented, which illustrate the correction and efficiency of the proposed method.