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Let's take a directed graph, or a digraph, $G=(V,E)$ given by a finite set of vertices $V$ and a finite set of edges $E$. We can assume that pairs of vertices can have parallel edges between them and ...

Let $G$ be a finite directed acyclic graph. The Cartan matrix $C_G=C$ of $G$ is defined as the matrix with rows and colums indexed by the vertices of $G$ and $c_{i,j}$ counts the number of paths from $...

Given a (simple) graph $G=(V,E)$ with $V=\{1,...,n\}$ and let $A$ be its adjacency matrix. I am interested in the representation theory (over $\Bbb R$) of the automorphism group $\def\Aut{\mathrm{Aut}...

Let $A$ be the adjacency matrix of an $r$-regular graph $G$ with $n$ vertices (Not complete or cycle graph) . Also, let $Aut(G)$ be the set of all its automorphisms (i.e. set of permutation matrices)....