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An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

Every graph with n vertices and maximum vertex degree Delta(G)<=k is (k+1)-colorable with all color classes of size |_n/(k+1)_| or [n/(k+1)], where |_x_| is the floor ...

Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

The Bron-Kerbosch algorithm is an efficient method for finding all maximal cliques in a graph.

A node which is one graph edge further away from a given node in a rooted tree.

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A hypergraph is a graph in which generalized edges (called hyperedges) may connect more than two nodes.

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...

A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...