2025/04/20 by Hechao Liu, Lu Li, Liu, Hechao +7
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2504.15314
openalex publication_date 2025/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be a graph with vertex set V(H)=\v1, v2, ⋯, vk\. The generalized blow-up graph Hp1,…,pkq1,…,qk is constructed by replacing each vertex vi ∈ V(H) with the graph Gi = piKt ∪ qiK1(i=1,2,⋯,k), then connecting all vertices between Gi and Gj whenever vivj ∈ E(H). In this paper, we enumerate the spanning trees in generalized blow-up graphs Hp1, p2, ⋯, pkq1, q2, ⋯, qk, which extends the results of Ge [Discrete Appl. Math. 305 (2021) 145-153], Cheng, Chen and Yan [Discrete Appl. Math. 320 (2022) 259-269]. Furthermore, we determine the resistance distances and Kirchhoff indices of generalized blow-up graphs Hp1, p2, ⋯, pkq1, q2, ⋯, qk, which extends the results of Sun, Yang and Xu [Discrete Math. 348 (2025) 114327], Xu and Xu [Discrete Appl. Math. 362 (2025) 18-33], Ni, Pan and Zhou [Discrete Appl. Math. 362 (2025) 100-108].