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The vertex connectivity kappa(G) of a graph G, also called "point connectivity" or simply "connectivity," is the minimum size of a vertex cut, i.e., a vertex subset S subset= ...

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...

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 ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

A black bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...

A white bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...

Discrete Mathematics

A graph in which each graph edge is replaced by a directed graph edge, also called a digraph. A directed graph having no multiple edges or loops (corresponding to a binary ...