# Questions tagged [graph-theory]

Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

3,400 questions
163 views

62 views

### Infinite connected $k$-regular graphs

Is it true that for any integer $k\geq 3$ there are $\aleph_0$ many connected countably infinite, pairwise non-isomorphic $k$-regular graphs?
109 views

### Distance regular Cayley graphs on $Z_2^n$?

Let $Z_2^n$ be group $Z_2 \times Z_2 \times \cdots \times Z_2$ with operation Exclusive-or. I'd like to know if the $Cay(Z_2^n,S)$ for $S \subset Z_2^n \setminus \{0\}$ is distance regular graph or ...
I have a problem I am working on that can be reduced to the following case of edge coloring with a special condition. Let $G$ be a directed graph with infinite vertices that are colored with $m$ ...
For any simple, undirected graph $G$, let $L(G)$ denote its line graph. $G=(\mathbb{Z}, E)$ with $E = \{\{k, k+1\}:k\in \mathbb{Z}\}$ has the property that $G\cong L(G)$. Is there a connected ...