@article{Cheng2026, 
author = {Sujing Cheng and Jun Ge},
title = {Counting spanning trees in generalized        K    n  -chain/ring graphs},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {1701-1711},
keywords = {spanning tree, generalized Kn-chain/ring graph, graph transformation, vertex-weighted graph, complete split graph},
url = {https://www.sciopen.com/article/10.3934/math.2026071},
doi = {10.3934/math.2026071},
abstract = {Let        K    n   be the complete graph of order    n. Very recently, the number of spanning trees (the        N    S    T   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        N    S    T   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.}
}