Exploring structural properties of $k$-trees and block graphs
Combinatorics
2026-02-17 v1
Abstract
We present a new characterization of -trees based on their reduced clique graphs and -line graphs, which are block graphs. We explore structural properties of these two classes, showing that the number of clique-trees of a -tree equals the number of spanning trees of the -line graph of . This relationship allows to present a new approach for determining the number of spanning trees of any connected block graph. We show that these results can be accomplished in linear time complexity.
Keywords
Cite
@article{arxiv.2301.10805,
title = {Exploring structural properties of $k$-trees and block graphs},
author = {Lilian Markenzon and Allana S. S. Oliveira and Cybele T. M. Vinagre},
journal= {arXiv preprint arXiv:2301.10805},
year = {2026}
}
Comments
6 pages, 1 figure