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The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The (upper) clique number of a graph G, denoted omega(G), is the number of vertices in a maximum clique of G. Equivalently, it is the size of a largest clique or maximal ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The central point in a wheel graph W_n. The hub has degree n-1.