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Spanning trees of descendants of a complete graph

Derya Asaner, Sayonita Ghosh Hajra and Maryam Siddique

Vol. 15 (2022), No. 3, 475–488
Abstract

We study the spanning trees of descendants of a complete graph. We provide three different proofs, based on linear algebra, for computing the number of spanning trees. Our result generalizes an old result of Weinberg that computes the number of spanning trees of a particular descendant of a complete graph.

Keywords
complete graph, spanning trees, Weinberg formula
Mathematical Subject Classification
Primary: 05C30
Milestones
Received: 18 July 2021
Revised: 16 October 2021
Accepted: 27 November 2021
Published: 2 December 2022

Communicated by Kenneth S. Berenhaut
Authors
Derya Asaner
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States
Sayonita Ghosh Hajra
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States
Maryam Siddique
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States