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A graph vertex in a graph is said to be an odd node if its vertex degree is odd.

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 ...

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.

Let graph G have p points v_i and graph H have p points u_i, where p>=3. Then if for each i, the subgraphs G_i=G-v_i and H_i=H-u_i are isomorphic, then the graphs G and H are ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

A set of circuits going along the graph edges of a graph, each with an even number of graph edges, such that just one of the circuits passes through each graph vertex (Ball ...