3 papers
math.CO2026
A unimodular bijection between harmonic vectors of 2-isomorphic graphs
William Watkins
Let and be connected graphs that are 2-isomorphic. It is known that their Laplacian matrices are congruent by a unimodular matrix . In this paper we show (Thm. \ref{thm:…
math.GT2018
A note on Dehn colorings and invariant factors
Derek A. Smith, Lorenzo Traldi, William Watkins
If is an abelian group and is an integer, let be the subgroup of consisting of elements such that . We prove that if is a diagram of a…
math.CO2017
Planarity, duality and Laplacian congruence
Derek A. Smith, Lorenzo Traldi, William Watkins
We discuss the connections tying Laplacian matrices to abstract duality and planarity of graphs.