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A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

A triangle-free graph is a graph containing no graph cycles of length three. A simple graph is triangle-free iff Tr(A^3)=0, where A is the adjacency matrix of the graph and ...

A concave polygon is a polygon that is not convex. A simple polygon is concave iff at least one of its internal angles is greater than 180 degrees. An example of a non-simple ...

The nth partial denominator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) or simple continued fraction b_0+K_(n=1)^infty1/(b_n) is the expression b_n. For ...

The strongly embedded theorem identifies all simple groups with a strongly 2-embedded subgroup. In particular, it asserts that no simple group has a strongly 2-embedded ...

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...

Barnette's conjecture asserts that every 3-connected bipartite cubic planar graph is Hamiltonian. The only graph on nine or fewer vertices satisfying Barnette's conditions is ...

The Cameron graph is a strongly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(231,30,9,3). It is distance-regular with intersection array ...

A cubic nonplanar graph is a graph that is both cubic and nonplanar. The following table summarizes some named nonplanar cubic graphs. graph G |V(G)| utility graph 6 Petersen ...