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A cycle double cover of an undirected graph is a collection of cycles that cover each edge of the graph exactly twice. For a polyhedral graph, the faces of a corresponding ...

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? ...

A closed trail is called a circuit when it is specified in cyclic order but no first vertex is explicitly identified.

Let c_k be the number of edge covers of a graph G of size k. Then the edge cover polynomial E_G(x) is defined by E_G(x)=sum_(k=0)^mc_kx^k, (1) where m is the edge count of G ...

Two nodes connected to the same node which are same distance from the root vertex in a rooted tree are called siblings. A function to return the siblings of a vertex v in a ...

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

An E_8 polytope is a polytope having the symmetry of the exceptional simple Lie groups E_8 of dimension 248. There are 255 uniform polytopes with E_8 symmetry in 8 ...

The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...

The mathematical study of the properties of the formal mathematical structures called graphs.

The multiplicity of a multigraph is its maximum edge multiplicity.