Resistance distance-based graph invariants and spanning trees of graphs derived from the strong product of P₂ and C_n

2019/06/11 by Yingui Pan, Jianping Li, Pan, Yingui +1 · 1 citation
Chemistry · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Metal-Organic Frameworks: Synthesis and Applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1906.04339

openalex publication_date 2019/06/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let G_n be a graph obtained by the strong product of P₂ and C_n, where n\geqslant3. In this paper, explicit expressions for the Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning trees of G_n are determined, respectively. It is surprising to find that the Kirchhoff (resp. multiplicative degree-Kirchhoff) index of G_n is almost one-sixth of its Wiener (resp. Gutman) index. Moreover, let G^r_n be the set of subgraphs obtained from G_n by deleting any r vertical edges of G_n, where 0\leqslant r\leqslant n. Explicit formulas for the Kirchhoff index and the number of spanning trees for any graph G^r_n∈ G^r_n are completely established, respectively. Finally, it is interesting to see that the Kirchhoff index of G^r_n is almost one-sixth of its Wiener index.

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• The normalized Laplacian, degree-Kirchhoff index and spanning trees of graphs derived from the strong prism of linear polyomino chain

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