# Questions tagged [algebraic-graph-theory]

Algebraic methods in Graph Theory; the linear algebra method, graph homomorphisms, group theoretic methods (for example Cayley graphs), and graph invariants. For graph eigenvalue problems use the spectral-graph-theory tag. For strongly regular graphs use the strongly-regular-graph tag. For Kneser graphs use the kneser-graph tag.

116 questions
Filter by
Sorted by
Tagged with
455 views

### Reference request: Moore graphs

It is clear that the term Moore graph was coined by Hoffman and Singleton in their paper On Moore graphs with diameters $2$ and $3$, where they write E. F. Moore has posed the problem of describing ...
347 views

### An algebraic view of graph reconstruction

$\DeclareMathOperator\Sym{Sym}\DeclareMathOperator\Coh{Coh}$I have broken my question into a few sections for clarity and to provide sufficient context to the problem. I apologize for the length. The ...
1 vote
101 views

1 vote
115 views

### Lower bound for $\vert \det A \vert$ for the adjacency matrix of regular graphs

Assume $G$ is a simple $k$-regular graph of order $n$ with adjacency matrix $A$ which is non-singular. Does anyone know some lower bounds for $\vert \det (A) \vert$ with respect to $n$, $k$ or both? ...
154 views

279 views

### Spectra of the quotient of a directed graph

Given a graph $G(V,E)$ and a partition $\{V_1,\dots V_n\}$ of the nodes set $V$, the adjacency and Laplacian spectra of the quotient graph $Q(G)$ interlaces the adjacent and the Laplacian spectra of ...
374 views

### Counting graphs according to recursion depth

Consider the set $S$ of multigraphs defined recursively as follows: Example Graph Class A graph $G$ is in $S$ if(f) $G$ is a loop on a single vertex, or $G$ may be obtained by ...
404 views

### A different avatar of the complexity of a graph

Let $G$ be a connected, finite graph. (For me a graph is undirected, and it possibly has multiple edges, although the latter is not really crucial for this question). The complexity $c(G)$ (also known ...
197 views

### Computing canonical forms from orbit partitions

Suppose we know the orbit partition of the vertices of a graph (due to the action of its automorphism group). Is it easy (as in "polynomial time") to generate a canonical form (aka "canonical labeling"...
Suppose I have two simplicial complexies $\triangle_1$ and $\triangle_2$. Consider their Stanley-Reisner ideals $I(\triangle_1)$ and $I(\triangle_2)$. I want to get their intersections when they meet ...
Suppose we have a simple connected graph $G=(V,E)$. Then let $A$ be its $|E|\times |V|$ incidence matrix. Here I am considering the unoriented incidence matrix. I want to know when the row span of $A$ ...