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A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...

An edge automorphism of a graph G is a permutation of the edges of G that sends edges with common endpoint into edges with a common endpoint. The set of all edge ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a ...

Let R+B be the number of monochromatic forced triangles (where R and B are the number of red and blue triangles) in an extremal graph. Then R+B=(n; 3)-|_1/2n|_1/4(n-1)^2_|_|, ...

The 600-cell is the finite regular four-dimensional polytope with Schläfli symbol {3,3,5}. It is also known as the hypericosahedron or hexacosichoron. It is composed of 600 ...