W. Watkins

activity

20082026

most citedSum of squares of degrees in a graph

28 citations · 28 across the 3 of their papers we have counts for

collaborators

4 papers

math.CO2026

A unimodular bijection between harmonic vectors of 2-isomorphic graphs

William Watkins

Let $G$ and $H$ be connected graphs that are 2-isomorphic. It is known that their Laplacian matrices are congruent by a unimodular matrix $U$ . 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 $A$ is an abelian group and $ϕ$ is an integer, let $A (ϕ)$ be the subgroup of $A$ consisting of elements $a \in A$ such that $ϕ \cdot a = 0$ . We prove that if $D$ 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.

math.CO2008★ 28 cited

Sum of squares of degrees in a graph

Bernardo M. Ábrego, Silvia Fernández-Merchant, Michael G. Neubauer +1

Let $\G(v,e)$ be the set of all simple graphs with $v$ vertices and $e$ edges and let $P_{2} (G) = \sum d_{i}^{2}$ denote the sum of the squares of the degrees, $d_{1}, > ..., d_{v}$ , of the ver…