Resistance distance-based graph invariants and spanning trees of graphs derived from the strong prism of a star

Zhemin Li, Zheng Xie, Jianping Li and Yingui Pan

Applied Mathematics and Computation, 2020, vol. 382, issue C

Abstract: Let Sn2 be the graph obtained by the strong prism of a star Sn, i.e. the strong product of K2 and Sn. In this paper, explicit expressions for Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning tress of Sn2 are determined, respectively. More specially, let Sn,r2 be the set of subgraphs obtained by randomly deleting r vertical edges from Sn2, where 0 ≤ r ≤ n. Explicit formulas for Kirchhoff index and number of spanning trees for any graph Sn,r2∈Sn,r2 are established, respectively. Moreover, the Kirchhoff index of Sn,r2 is almost three-eighths of its Wiener index.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303015

DOI: 10.1016/j.amc.2020.125335

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