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Results tagged with trees
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user 10881
A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
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. …
- 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
3
votes
Grassmannian cluster algebra of infinite type has no trees in its mutation class
The quivers are almost trees, and only have one double edge and three oriented triangles. …
- 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. … Bauer, "On vertex covers, matchings and random trees"
Let me briefly define this coloring (using my own choice of colors). …
- 3,597