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Results tagged with graph-theory
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user 10881
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.
4
votes
How can I prove that a particular family of graphs is integral?
As a service, here is a sage program.
def G(n, k):
"""
Mathoverflow Question 159022
"""
vertices = Words(range(k + 1), n)
vertices = [w for w in vertices if w.count(ZZ(0)) == 1]
…
- 3,597
3
votes
Is the following invariant of rooted trees a complete invariant?
The number of different values taken by the polynomial is given by
1, 1, 2, 4, 9, 20, 47, 112, 274, 679, 1717, ...
Comparing with the sequence A000081 given by
1, 1, 2, 4, 9, 20, 48, 115, 286, 719, …
- 3,597
4
votes
Characteristic polynomials of trees and E8
Using sage, and up to 16 vertices included, one finds only two trees satisfying $|det(A+2I)|=1$, namely $E_8$ and $E_{10}$.
EDIT: I also confirm that there are 18 such trees with 18 vertices. Here th …
- 3,597
6
votes
Genus of Tutte-Coxeter Graph
According to sage, the genus is 4
sage: T = graphs.TutteCoxeterGraph()
sage: T.genus()
4
- 3,597
2
votes
Number of trees with the same matching number
This can be done using the canonical coloring of vertices of trees into 3 colors that can be found in
J. Zito, "The structure and maximum number of maximum independent sets in trees"
S. Coulomb and …
- 3,597
1
vote
Flow of an integer
As a service to the community, here are these digraphs in sage:
def divisor_graph(n):
"""
Mathoverflow 159319
"""
vert = divisors(n)
return DiGraph([(a, b, b / a) for b in vert
…
- 3,597