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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Correspondence between matrix multiplication and a graph operation of Lovász

In his book "Large networks and graph limits", Lovász describes a multiplication operation (he calls it concatenation) on "bi-labeled graphs". An $(m,n)$ bi-labeled graph is a ...
David Roberson's user avatar
8 votes
2 answers
560 views

Does the clique-coclique bound hold for all walk-regular graphs?

The clique-coclique bound is said to hold for a simple graph $G$ on $n$ vertices if $\lvert \omega(G) \rvert \lvert \alpha(G) \lvert \leq n$, letting $\omega(G)$ and $\alpha(G)$ denote its clique and ...
m4farrel's user avatar
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7 votes
2 answers
409 views

Automorphism group of a special commuting graph

Suppose $S_6$ is the symmetric group on six letters and let $X$ denote the conjugacy class containing $(12)(34)$. Define a graph $\Gamma$ with vertex set $X$ and edges precisely the 2-element subsets ...
maryam's user avatar
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7 votes
4 answers
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Cayley graphs and its subgraphs

I have two questions about Cayley graphs. Any answers will be appreciate. 1) Do we have any Cayley graph that has Petersen graph as its induced subgraph? 2) Suppose $Cay(G,S)$ be a Cayley graph that ...
Shahrooz's user avatar
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5 votes
2 answers
391 views

Condition(s) for the full autormophism group $\operatorname{Aut}(C(G, S))$ of the Cayley graph of $G$ to be isomorphic to $G$

If $\Gamma = C(G, S)$ is the (undirected) Cayley graph of a finite group $G$ with generating set $S$, then $G \le \operatorname{Aut}(\Gamma)$, the "full" automorphism group of $\Gamma$. When is it ...
M. Vinay's user avatar
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5 votes
1 answer
139 views

Inertia of a class of Cayley graphs

Let $H^n_2(d)$ be the Cayley graph with vertex set $\{0,1\}^n$ where two strings form an edge iff they have Hamming distance at least $d$. What is the inertia of these graphs, that is, the numbers of ...
Clive elphick's user avatar