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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.

1 vote
1 answer
281 views

A computation problem of algebraic connectivity of a tree

The algebraic connectivity of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to …
Tylar Liu's user avatar
4 votes
3 answers
10k views

power of adjacency matrix

Suppose A is the adjacency matrix of a graph G. It is well known that the number of walks of length $\ell$ in G, from $v_i$ to $v_j$, is the entry in position $(i,j)$ of the matrix $A^\ell$. My questi …
Tylar Liu's user avatar