# 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.

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### Varieties determined by a characteristic-type of polynomial with the structure of an underlying graph

While writing my master thesis, following problem came up: Given a digraph $G$ with edges $e_1,..,e_n$ and a given a $n\times n$- matrix $A\in\mathbb{C}^{n\times n}$ such that $A_{ij}=0$ if the ending ...
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### The rank of a Laplacian-type matrix

Suppose that $M$ is an integer, symmetric matrix of order $n>2$ with the positive integers $K_1,\dotsc,K_n$ on its main diagonal, and with all the off-diagonal elements equal to $0$ or $1$ so that ...
How do I find eigenvalues for the adjacency matrix of Cayley graph $X(S_n,S)$ where $S_n$ is the symmetric group of order $n$ and $S$ is the set of transpositions $(i,i+1)$, if the eigenvalues of the ...