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A335790 Triangle read by rows of possible absolute values of alternating sums when traveling around a tree with n edges, with each node labeled with the number of edges connected to it, until each edge has been visited twice. 0
0, 2, 0, 6, 2, 4, 12, 0, 2, 6, 10, 20, 0, 2, 4, 6, 8, 10, 12, 18, 30, 0, 2, 4, 6, 8, 10, 14, 16, 20, 28, 42, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 22, 24, 26, 30, 40, 56, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 36, 38, 42, 54, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Begin and end on the same node, but do not include the ending step in the sum.
Two isomorphic trees will always have the same alternating sum, because flipping branches around will always switch two odd-length sequences separated by another odd-length sequence (the reverse is NOT true in general - flipping sequences around is not even guaranteed to create a tree).
Trees which are symmetric around an edge will have alternating sum 0, because the same numbers appear on either side of that edge.
Two graphs can have the same alternating sum, and the same sum, and still not be isomorphic.
LINKS
EXAMPLE
For the tree of length 2, 1-2+1-2 = -2. The tree is described by [1,2,1,2].
First five rows of the triangle:
0
2
0, 6
2, 4, 12
0, 2, 6, 10, 20
CROSSREFS
Sequence in context: A140876 A243997 A036044 * A078991 A346790 A217572
KEYWORD
nonn,tabf
AUTHOR
Michael Arnold, Jun 23 2020
STATUS
approved

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Last modified April 24 00:30 EDT 2024. Contains 371917 sequences. (Running on oeis4.)