Profile directory About Mobile apps
Log in Sign up
arXiv Math @arxiv_math@qoto.org
Follow

Enumeration of spanning trees and resistance distances of generalized blow-up graphs https://arxiv.org/abs/2504.15314 #mathCO

Enumeration of spanning trees and resistance distances of generalized blow-up graphs

Let $H$ be a graph with vertex set $V(H)=\{v_1, v_2, \cdots, v_k\}$. The generalized blow-up graph $H_{p_1,\ldots,p_k}^{q_1,\ldots,q_k}$ is constructed by replacing each vertex $v_i \in V(H)$ with the graph $G_i = p_iK_t \cup q_iK_1$$(i=1,2,\cdots,k)$, then connecting all vertices between $G_i$ and $G_j$ whenever $v_iv_j \in E(H)$. In this paper, we enumerate the spanning trees in generalized blow-up graphs $H_{p_1, p_2, \cdots, p_k}^{q_1, q_2, \cdots, q_k}$, 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 $H_{p_1, p_2, \cdots, p_k}^{q_1, q_2, \cdots, q_k}$, 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].

arXiv.org
April 24, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
Sign in to participate in the conversation
Qoto Mastodon

QOTO: Question Others to Teach Ourselves
An inclusive, Academic Freedom, instance
All cultures welcome.
Hate speech and harassment strictly forbidden.

Trending now

#news0 people talking
0

Resources

  • Terms of service
  • Privacy policy

Developers

  • Documentation
  • API

What is Mastodon?

qoto.org

  • About
  • v3.5.19-qoto

More…

  • Source code
  • Mobile apps
v3.5.19-qoto · Privacy policy