AcyclicQ[g] yields True if graph g is acyclic.
Automorphisms[g] gives the automorphism group of the graph g.
BipartiteQ[g] yields True if graph g is bipartite.
Brelaz
(Combinatorica Package Symbol) Brelaz is a value that the option Algorithm can take when used in the function VertexColoring.
CartesianProduct[l_1, l_2] gives the Cartesian product of lists l_1 and l_2.
ChvatalGraph returns a smallest triangle-free, 4-regular, 4-chromatic graph.
CircularEmbedding[n] constructs a list of n points equally spaced on a circle. CircularEmbedding[g] embeds the vertices of g equally spaced on a circle.
CliqueQ
(Combinatorica Package Symbol) CliqueQ[g, c] yields True if the list of vertices c defines a clique in graph g.
Cofactor[m, {i, j}] calculates the (i, j)\[Null]^th cofactor of matrix m.
CompleteBinaryTree[n] returns a complete binary tree on n vertices.