The number of -matchings in almost every tree is a zero residue.
The number of graphs not containing as a minor.
The number of isomorphism classes of spanning trees of a graph
The number of knight's tours equals 33, 439, 123, 484, 294—counting with binary decision diagrams.
The number of labeled 2-connected planar graphs.
The Number of Labeled Dissections of a k-Ball.
The number of labelled -arch graphs.
The Number of Non-Isomorphic Hamiltonian Circuits in an -Dimensional Cube
The number of spanning trees and chains of graphs.
The number of spanning trees of double graphs
The number of triangles in a tringulation of a set of points in the plane.
The order of monochromatic subgraphs with a given minimum degree.
The order of uniquely partitionable graphs
Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition V₁,...,Vₙ of V(G) such that, for each i = 1,...,n, the subgraph of G induced by has property . If a graph G has a unique (₁,...,ₙ)-partition we say it is uniquely (₁,...,ₙ)-partitionable. We establish best lower bounds for the order of uniquely (₁,...,ₙ)-partitionable graphs, for various choices of ₁,...,ₙ.
The orderings of bicyclic graphs and connected graphs by algebraic connectivity.
The orientability of the direct product of graphs
The outer-distance of nodes in random trees.
The -matrix completion problem.
The packing and covering of the complete graph. I: The forests of order five.
The path is the tree with smallest greatest Laplacian eigenvalue
The path polynomial of a complete graph.