Counting spanning trees in generalized $ K_n $-chain/ring graphs
Abstract
Let $ K_n $ be the complete graph of order $ n $. Very recently, the number of spanning trees (the $ \mathcal{NST} $ for short) and the resistance distances in $ K_n $-chain (ring) graphs were determined explicitly. We generalized the concept to the generalized $ K_n $-chain (ring) graph $ [L_n^s]^m $ ($ [C_n^s]^m $). New formulae for the $ \mathcal{NST} $ of $ [L_n^s]^m $ and $ [C_n^s]^m $ were given by a simple and more physical way with a novel technique of adding a pair of positive and negative edges, avoiding complicated linear algebraic computations.
Fields of Study & Subjects
Graph theory and applications
Stochastic processes and statistical mechanics
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 1
- Pages
- 1701–1711
- Publication date
- 1 January 2026