All Questions

Let $A$ be the directed adjacency matrix of an acyclic directed graph, with variables as its nonzero entries (one for each edge). The $(a,b)$ entry of the matrix $(I-A)^{-1}$ is the sum over all paths ...

Consider simple graphs. Any simple graph $G$ is called nonsingular if its $(0,1)$-adjacency matrix $A(G)$ has nonzero determinant. Does there exist any nonsingular simple graph whose determinant value ...

It is well known that the number of (cyclic) De Bruijn sequences is $2^{2^{n-1}-n}$. This number may also be interpreted as the number of cycles of length $2^n$ in the De Bruijn graph of order $n$. ...

Let $(V,E)$ be a finite oriented directed graph, with vertices and edges ordered, and $M$ the $|V|\times |E|$ matrix with entries $$ m_{ve} = \begin{cases} 1 &\text{if $e$ points at $v$}\\ -1 &...

We have a simple graph with vertices $\{v_1, v_2, ... v_n\}$. The adjacency matrix of this graph is $A= (a_{ij})$ so that $a_{ij}=1$ if $i+j$ belongs to the Fibonacci sequence; $a_{ij}=0$ ...