Counting Isomorphism Classes of Spanning Trees of Complete Bipartite Graphs

Peter Johnson; Shayne Nochumson

Counting Isomorphism Classes of Spanning Trees of Complete Bipartite Graphs

Combinatorics 2026-03-03 v2

Authors: Peter Johnson , Shayne Nochumson

Abstract

Spanning trees of complete bipartite graphs exhibit a rich interaction between degree sequences and graph structure. In this paper, we obtain lower bounds on the number of isomorphism classes of spanning trees in $K_{a,b}, 2 \leq a \leq b$ in terms of $P_a(a+b-1)$ and $P_b(a+b-1)$ where $P_k(m)$ is the number of integer partitions of $m$ of length $k$ . Furthermore, we obtain an upper bound in terms of $a$ and $b$ .

Keywords

spanning trees isomorphism classes complete bipartite graphs integer partitions graph enumeration

Cite

@article{arxiv.2602.06867,
  title  = {Counting Isomorphism Classes of Spanning Trees of Complete Bipartite Graphs},
  author = {Peter Johnson and Shayne Nochumson},
  journal= {arXiv preprint arXiv:2602.06867},
  year   = {2026}
}

Comments

5 pages, 3 figures

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