Wedderburn-Etherington number

Encyclopedia

In graph theory

, the

and Joseph Wedderburn

, count how many weak binary tree

s can be constructed: that is, the number of trees for which each graph vertex

(not counting the root) is adjacent to no more than three other such vertices, for a given number of node

s. The first few Wedderburn–Etherington numbers are

Graph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, the

**Wedderburn–Etherington numbers**, named for Ivor Malcolm Haddon EtheringtonIvor Malcolm Haddon Etherington

Ivor Malcolm Haddon Etherington was a mathematician who worked initially on general relativity, but later moved into genetics where he introduced genetic algebras.-References:...

and Joseph Wedderburn

Joseph Wedderburn

Joseph Henry Maclagan Wedderburn was a Scottish mathematician, who taught at Princeton University for most of his career. A significant algebraist, he proved that a finite division algebra is a field, and part of the Artinâ€“Wedderburn theorem on simple algebras...

, count how many weak binary tree

Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two child nodes, usually distinguished as "left" and "right". Nodes with children are parent nodes, and child nodes may contain references to their parents. Outside the tree, there is often a reference to...

s can be constructed: that is, the number of trees for which each graph vertex

Vertex (graph theory)

In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs...

(not counting the root) is adjacent to no more than three other such vertices, for a given number of node

Vertex (graph theory)

In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs...

s. The first few Wedderburn–Etherington numbers are

- 1, 1, 1, 2, 3, 6, 1111 (number)11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name...

, 2323 (number)23 is the natural number following 22 and preceding 24.- In mathematics :Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime...

, 4646 (number)46 is the natural number following 45 and preceding 47.- In mathematics :Forty-six is a Wedderburn-Etherington number, an enneagonal number and a centered triangular number. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that can't be expressed...

, 9898 (number)98 is the natural number following 97 and preceding 99.-In astronomy:* Messier 98, a magnitude 11.0 spiral galaxy in the constellation Coma Berenices....

, 207, 451, 983, 2179, 4850, 10905, 24631, 56011, 127912, 293547, 676157, 1563372, 3626149, 8436379, 19680277, 46026618, 107890609, 253450711, 596572387, 1406818759, 3323236238, 7862958391,...