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The coloring red of two complete subgraphs of n/2 points (for even n) in order to generate a blue-empty graph.

The set of all edge automorphisms of G, denoted Aut^*(G). Let L(G) be the line graph of a graph G. Then the edge automorphism group Aut^*(G) is isomorphic to Aut(L(G)), ...

A number of graphs are associated with P. J. Owens. The 76-node Owens graph (Owens 1980) provides the smallest known example of a polyhedral quintic nonhamiltonian graph. It ...

A forest is an acyclic graph (i.e., a graph without any graph cycles). Forests therefore consist only of (possibly disconnected) trees, hence the name "forest." Examples of ...

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

The Paulus graphs are the 15 strongly regular graphs on 25 nodes with parameters (nu,k,lambda,mu)=(25,12,5,6) and the 10 strongly regular graphs on 26 nodes with parameters ...

The disorder number of a simple connected graph on n vertices is defined as the maximum length of a walk along the edges of the graph taken over all ordering of its vertices ...

Every nonplanar graph contains either the utility graph K_(3,3) (i.e., the complete bipartite graph on two sets of three vertices) or the pentatope graph K_5 as a ...

A minimum edge cut of a graph is an edge cut of smallest possible size. The size of a minimum edge cut in a connected graph G is called the graph's edge connectivity ...

A vertex-induced subgraph (sometimes simply called an "induced subgraph") is a subset of the vertices of a graph G together with any edges whose endpoints are both in this ...