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Given a weighted, undirected graph G=(V,E) and a graphical partition of V into two sets A and B, the cut of G with respect to A and B is defined as cut(A,B)=sum_(i in A,j in ...

A minimal dominating set is a dominating set in a graph that is not a proper subset of any other dominating set. Every minimum dominating set is a minimal dominating set, but ...

A strongly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in the direction(s) in which they ...

The Laplacian spectral radius of a finite graph is defined as the largest value of its Laplacian spectrum, i.e., the largest eigenvalue of the Laplacian matrix (Lin et al. ...

A minimal vertex cut is an vertex cut of a graph that is not a proper subset of any other vertex cut. Every minimum vertex cut is a minimal vertex cut, but the converse does ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...

Dirac (1952) proved that if the minimum vertex degree delta(G)>=n/2 for a graph G on n>=3 nodes, then G contains a Hamiltonian cycle (Bollobás 1978, Komlós et al. 1996). In ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...