On some classes of bivalent and trivalent planar graphs
Combinatorics
2025-05-20 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
A graph is called bivalent or trivalent if there exists an eigenvector of the graph Laplacian composed from {-1,1} or {-1,0,1}, respectively. These bivalent and trivalent eigenvectors are important for engineering applications, in particular for vibrating systems. In this article, we determine the structure of bivalent and trivalent graphs in the following planar graph families: trees, unicyclic, bicyclic, and cactus.
Cite
@article{arxiv.2505.13199,
title = {On some classes of bivalent and trivalent planar graphs},
author = {Jorge Alencar and Jean-Guy Caputo and Leonardo de Lima and Arnaud Knippel},
journal= {arXiv preprint arXiv:2505.13199},
year = {2025}
}