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The assignment of labels or colors to the edges or vertices of a graph. The most common types of graph colorings are edge coloring and vertex coloring.

The Kummer graph is the name apparently first adopted here for the Levi graph of Kummer's 16_6 configuration (Coxeter 1950), corresponding to the folded 6-cube graph (Brouwer ...

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

Let (P,B) denote a configuration with v points P={p_1,...,p_v} and b lines ("blocks") B=(B_1,...,B_b). Then the Levi graph L(P,B), also called the incidence graph, of a ...

The graph product denoted G-H and defined by the adjacency relations (gadjg^') or (g=g^' and hadjh^'). The graph lexicographic product is also known as the graph composition ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...

The Wells graph, sometimes also called the Armanios-Wells graph, is a quintic graph on 32 nodes and 80 edges that is the unique distance-regular graph with intersection array ...

"The" square graphs is the cycle graph C_4. It is isomorphic to the complete bipartite graph K_(2,2). Like all cycle graphs, the line graph of C_4 is isomorphic to itself. A ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...