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An imperfect graph G is a graph that is not perfect. Therefore, graphs G with omega(G)<chi(G) (1) where omega(G) is the clique number and chi(G) is the chromatic number are ...

A unit-distance embedding is a graph embedding in which all edges have unit length. A graph possessing a unit-distance embedding in two dimensions is called a unit-distance ...

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect. ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

The graph tensor product, also called the graph cardinal product (Imrich 1998), graph categorical product, graph conjunction, graph direct product (Hammack et al. 2016), ...

A polyhedral graph having 10 vertices. There are 32300 nonisomorphic nonahedral graphs, as first enumerated by Duijvestijn and Federico (1981).

A quartic nonhamiltonian graph is a quartic graph that is nonhamiltonian. A number of such graphs are illustrated above. Van Cleemput and Zamfirescu (2018) gave a 39-vertex ...

The Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage (Read and Wilson 1998, p. 273). Like the other (5,5)-cages, the Robertson-Wegner ...