Year: 2025
Type: preprint
Abstract: Substituting each edge of a simple connected graph $G$ by a path of length 1 and $k$ paths of length 5 generates the $k$-hexagonal graph $H^k(G)$. Iterative graph $H^k_n(G)$ is produced when the preceding constructions are repeated $n$ times. According to the graph structure, we obtain a set of linear equations, and derive the entirely normalized Laplacian spectrum of $H^k_n(G)$ when $k = 1$ and $k \geqslant 2$ respectively by analyzing the structure of the solutions of these linear equations. We find significant formulas to calculate the Kemeny's constant, multiplicative degree-Kirchhoff index and number of spanning trees of $H^k_n(G)$ as applications.
Source: arXiv (Cornell University)
Authors: Li, Hao, Chen, Xinyi, Liu, Hao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1347097983
OpenAlex ID: W4417090380
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