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For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

The girth of a graphs is the length of one of its (if any) shortest graph cycles. Acyclic graphs are considered to have infinite girth (Skiena 1990, p. 191). The girth of a ...

A straight line embedding, or "straight line drawing," of a graph is a graph embedding in which all edges are drawn as straight line segments (as opposed to curves, etc.).

The central point in a wheel graph W_n. The hub has degree n-1.

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

The group C_2×C_2×C_2 is one of the three Abelian groups of order 8 (the other two groups are non-Abelian). An example is the modulo multiplication group M_(24) (which is the ...

A quantitative measure of the simplicity of a geometric construction which reduces geometric constructions to five steps. It was devised by È. Lemoine. S_1 Place a ...

There are several different definition of link. In knot theory, a link is one or more disjointly embedded circles in three-space. More informally, a link is an assembly of ...

The small dodecahemidodecahedron is the uniform polyhedron with Maeder index 51 (Maeder 1997), Wenninger index 91 (Wenninger 1989), Coxeter index 65 (Coxeter et al. 1954), ...