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A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all ...

Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other. This is the Wallace-Bolyai-Gerwien theorem. For minimal ...

Let f be a fractional coloring of a graph G. Then the sum of values of f is called its weight, and the minimum possible weight of a fractional coloring is called the ...

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 ...

The (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...