The normalized Laplacian spectra of subdivision vertex-edge neighbourhood vertex(edge)-corona for graphs

2018/06/26 by Fei Wen, You Zhang, Wen, Fei +3
Chemistry · Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1806.10133

openalex publication_date 2018/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce two new graph operations, namely, the subdivision vertex-edge neighbourhood vertex-corona and the subdivision vertex-edge neighbourhood edge-corona on graphs G₁, G₂ and G₃, and the resulting graphs are denoted by G₁^S\bowtie (G₂^V∪ G₃^E) and G₁^S\diamondsuit(G₂^V∪ G₃^E), respectively. Whereafter, the normalized Laplacian spectra of G₁^S\bowtie (G₂^V∪ G₃^E) and G₁^S\diamondsuit(G₂^V∪ G₃^E) are respectively determined in terms of the corresponding normalized Laplacian spectra of the connected regular graphs G₁, G₂ and G₃, which extend the corresponding results of [A. Das, P. Panigrahi, Linear Multil. Algebra, 2017, 65(5): 962-972]. As applications, these results enable us to construct infinitely many pairs of normalized Laplacian cospectral graphs. Moreover, we also give the number of the spanning trees, the multiplicative degree-Kirchhoff index and Kemeny's constant of G₁^S\bowtie (G₂^V∪ G₃^E) (resp. G₁^S\diamondsuit(G₂^V∪ G₃^E)).

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