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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.

7 votes
1 answer
585 views

Local complementation group of simple graphs

This is my first time posting a question, so please excuse me for any incomplete or confusing descriptions. Let's assume we start with one simple graph(no multi-edges and no loops of a vertex to its …
P.H.'s user avatar
  • 141
2 votes
0 answers
244 views

Group of local complementation as a coxeter group

Can the group generated by local complementations, ${lc_i|i=1,\cdots,n}$ on simple graphs on $n$ vertices, be categorized as a coxeter group? After all these obey: \begin{equation} \langle lc_i| (lc_ …
P.H.'s user avatar
  • 141
0 votes

What is the n-th power of the adjacency matrix equal to?

I would need to know what exactly is the definition you are using for a "path" and not a "walk", based on which this answer may be either useful or useless. But the $n^{th}$ power of the adjacency mat …
P.H.'s user avatar
  • 141