An arithmetical structure on a finite, connected graph G is a pair of vectors (d, r) with positive
integer entries for which (diag (d)− A) r= 0, where A is the adjacency matrix of G and where …

In this note we introduce a finite abelian group that can be associated with any finite
connected graph. This group can be defined in an elementary combinatorial way in terms of …

Let G be a connected undirected graph on n vertices with no loops but possibly multiedges.
Given an arithmetical structure (r, d) on G, we describe a construction which associates to it …

arXiv:1903.01398v1 [math.CO] 4 Mar 2019 Page 1 arXiv:1903.01398v1 [math.CO] 4 Mar
2019 Arithmetical Structures on Paths With a Doubled Edge Darren Glass & Joshua …

Let $ G $ be a finite, connected graph. An arithmetical structure on $ G $ is a pair of positive
integer-valued vectors $(\mathbf {d},\mathbf {r}) $ such that $(\text {diag}(\mathbf {d}) …

An arithmetical structure on a finite, connected graph without loops is an assignment of
positive integers to the vertices that satisfies certain conditions. Associated to each of these …

An arithmetical structure on a finite, connected graph without loops is given by an
assignment of positive integers to the vertices such that, at each vertex, the integer there is a …

An arithmetical structure on a finite, connected graph G is a pair of vectors (d, r) with positive
integer entries for which (diag (d)− A (G)) r T= 0, where diag (d)= diag (d 1, d 2,…, dn), A (G) …

Given a graph G, an arithmetical structure on G is a pair of positive integer vectors (d, r) such
that gcd (rv| v∈ V (G))= 1 and (diag (d)− A) r= 0, where A is the adjacency matrix of G. We …

An arithmetical structure on the complete graph K n with n vertices is given by a collection of
n positive integers with no common factor, each of which divides their sum. We show that, for …