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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 word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...

Tutte (1971/72) conjectured that there are no 3-connected nonhamiltonian bicubic graphs. However, a counterexample was found by J. D. Horton in 1976 (Gropp 1990), and several ...

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...

A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

As proposed by Hosoya (1971), the Hosoya index (also called Z-index) of a graph is defined by Z = sum_(k=0)^(n)|a_k| (1) = sum_(k=0)^(n)b_k, (2) where n is the number of ...

There are two distinct notions of connectivity in a directed graph. A directed graph is weakly connected if there is an undirected path between any pair of vertices, and ...

The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...

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 ...