
Chvátal conjectured that if
R.A. Bailey has conjectured that all finite groups except elementary Abelian
A set
We enumerate by computer algorithms all simple
Let
We consider certain resolvable designs which have applications to doubly perfect Cartesian authentication schemes. These generalize structures determined by sets of mutually orthogonal Latin squares and are related to semi-Latin squares and other designs which find applications in the design of experiments.
A
is shown. It is also shown that a
We consider the changing and unchanging of the edge covering and edge independence numbers of a graph when the graph is modified by deleting a node, deleting an edge, or adding an edge. In this paper, we present characterizations for the graphs in each of these classes and some relationships among them.
Let
We investigate the edge-gracefulness of
For
We prove that there exist precisely
The known generalized quadrangles with parameters
In this paper, we illustrate the relationship between profiles of Hadamard matrices and weight distributions of codes, give a new and efficient method to determine the minimum weight
We define an
We establish that every vertex of degree at least
We consider square arrays of numbers
We give generating functions and arithmetical relations for these numbers. We show that every row of such an array is eventually log concave, and give a few sufficient conditions for columns to be eventually log concave. We also give a necessary condition for a column to be eventually log concave, and provide examples to show that there exist such arrays in which no column is eventually log concave.
In this paper, we obtain some necessary conditions for the existence of balanced arrays (
It is shown that the circuit polynomial of a graph, when weighted by the number of nodes in the circuits, does not characterize the graph, i.e., non-isomorphic graphs can have the same circuit polynomial. Some general theorems are given for constructing graphs with the same circuit polynomial (cocircuit graphs). Analogous results can be deduced for characteristic polynomials.
Given
1970-2025 CP (Manitoba, Canada) unless otherwise stated.