All Questions

I am wondering if the following pair of cospectral graphs was previously known. The rhombic dodecahedron graph looks like this (graph6 string: 'M?????rrAiTOd_YO?'): As far as I know, it was previously ...

The orthogonality graph $\Omega(n)$ with $2^n$ vertices is the graph with vertex set $\{-1,+1\}^n$, with two vertices being adjacent if and only if they are orthogonal (as vectors in the standard ...

Let $A$ be a $0/1$ square matrix which can be permuted to a non singular or a singular lower triangular matrix. Determinant is either $0$ or $1$. Can we provide tighter upper bounds on its spectral ...

Let $(V,E)$ be an undirected, connected graph with $n$ nodes. The graph Laplacian is defined as $L = D - A$, where $D$ is the degree matrix and $A$ is the adjacency matrix. Let $0 = \lambda_1 < \...

Let $G$ be an undirected graph and the corresponding adjacency matrix be $A$. Let $v$ be a cut-vertex of $G$. Let $G_1, G_2,\dots, G_k$ are the connected components of the induced graph $G-v$ ( the ...

What relation, if any, is there between the singular values of the adjacency matrix ( or possibly incidence matrix) of a simple graph and its chromatic number. Typically, do we have Hoffmann type, or ...