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Let S be a set and F={S_1,...,S_p} a nonempty family of distinct nonempty subsets of S whose union is union _(i=1)^pS_i=S. The intersection graph of F is denoted Omega(F) and ...

The order-n bouquet graph B_n is a pseudograph consisting of a single vertex with n self-loops. The bouquet graph B_1 is a pseudograph that can be considered to correspond to ...

The n-sunlet graph is the graph on 2n vertices obtained by attaching n pendant edges to a cycle graph C_n (ISGCI), i.e., the coronas C_n circledot K_1 (Frucht 1979). Sunlet ...

Robertson's apex graph is the 15-vertex graph illustrated above constructed by Neil Robertson as an example of an apex graph that is not YDeltaY-reducible. The graph may be ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

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 ...

The rhombic dodecahedral graph is the Archimedean dual graph which is the skeleton of the rhombic dodecahedron (as well as the Bilinski dodecahedron). It is the Levi graph of ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

A quintic symmetric graph is a quintic graph (i.e., regular of degree 5) that is also symmetric. Since quintic graphs exist only on an even number of nodes, so do symmetric ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...