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Results tagged with graph-theory
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user 45250
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.
8
votes
Why do we associate a graph to a ring?
Let me give a slightly inflammatory analogy:
One finds that there are many ways to associate a group with a manifold, e.g. homotopy groups or homology groups. Many people work in this field, which ba …
2
votes
How to understand the combinatorial Laplacian $\Delta$ which is defined on the graph?
Fix a vertex $v$. Then
$$
\nabla F(uv) = c(u,v)\big(F(v)-F(u)\big)
$$
for $u$ adjacent to $v$. Now
\begin{align*}
\nabla\cdot\nabla F(v) &= \sum_{uv} c(v,u)\big(F(u)-F(v)\big)\\ &= -F(v)\left(\sum_u c …
- 3,065
1
vote
Can a Feynman graph be an empty set?
Consolidating from comments:
The definitions given in the question are a bit unusual, so it is not straightforward to interpret them.
However, best as I understand the question, it is not about whet …
- 3,065
12
votes
Line graphs called "graph derivatives": any intuition?
If one considers a graph $G=(V,E)$ and a function $f:V\to\mathbb{R}$, it makes sense to look at the finite differences $f(v_i)-f(v_j)$ for neighboring vertices $v_i,v_j\in V$ as a sort of discrete der …
- 3,065