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.
7
questions
11
votes
1
answer
436
views
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 ...
- 2,289
8
votes
2
answers
589
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 ...
- 155
7
votes
1
answer
445
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 ...
7
votes
4
answers
2k
views
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 ...
- 4,748
7
votes
2
answers
415
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 ...
- 81
5
votes
1
answer
144
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 ...
- 421
5
votes
2
answers
399
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 ...
- 178