A335790 - OEIS

%I #16 Aug 13 2020 21:57:44

%S 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,

%T 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,

%U 14,16,18,20,22,24,26,28,30,34,36,38,42,54,72

%N 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.

%C Begin and end on the same node, but do not include the ending step in the sum.

%C 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).

%C Trees which are symmetric around an edge will have alternating sum 0, because the same numbers appear on either side of that edge.

%C Two graphs can have the same alternating sum, and the same sum, and still not be isomorphic.

%e For the tree of length 2, 1-2+1-2 = -2. The tree is described by [1,2,1,2].

%e First five rows of the triangle:

%e 0

%e 2

%e 0, 6

%e 2, 4, 12

%e 0, 2, 6, 10, 20

%K nonn,tabf

%O 1,2

%A _Michael Arnold_, Jun 23 2020