15 research outputs found
An optimal marketing strategy for porkers with differences in growth rates and dependent prices
marketing;strategic planning;farms;agricultural economics
Mutually Orthogonal Latin Squares and Self-complementary Designs
Suppose that n is even and a set of n/2 -1 mutually orthogonal
Latin squares of order n exists. Then we can construct a strongly
regular graph with parameters (n², n/2 (n-1), n/2 ( n/2-1), n/2 ( n/2 -1)), which
is called a Latin square graph. In this paper, we give a sufficient condition
of the Latin square graph for the existence of a projective plane of
order n. For the existence of a Latin square graph under the condition,
we will introduce and consider a self-complementary 2-design (allowing
repeated blocks) with parameters (n, n/2 , n/2 ( n/2 -1)). For n ≡ 2 (mod 4),
we give a proof of the non-existence of the design.</p
Developments on Spectral Characterizations of Graphs
In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50Spectra of graphs;Cospectral graphs;Generalized adjacency matrices;Distance-regular graphs
Difference Covering Arrays and Pseudo-Orthogonal Latin Squares
Difference arrays are used in applications such as software testing,
authentication codes and data compression. Pseudo-orthogonal Latin squares are
used in experimental designs. A special class of pseudo-orthogonal Latin
squares are the mutually nearly orthogonal Latin squares (MNOLS) first
discussed in 2002, with general constructions given in 2007. In this paper we
develop row complete MNOLS from difference covering arrays. We will use this
connection to settle the spectrum question for sets of 3 mutually
pseudo-orthogonal Latin squares of even order, for all but the order 146
5-Chromatic Strongly Regular Graphs
In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5.Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph.For each parameter set, we must decide which strongly regular graphs, if any, possessing the set are 5-chromatic.In this way, we deal completely with 34 of these parameter sets using eigenvalue techniques and computer enumerations.graphs;eigenvalues
Equiangular lines in Euclidean spaces
We obtain several new results contributing to the theory of real equiangular
line systems. Among other things, we present a new general lower bound on the
maximum number of equiangular lines in d dimensional Euclidean space; we
describe the two-graphs on 12 vertices; and we investigate Seidel matrices with
exactly three distinct eigenvalues. As a result, we improve on two
long-standing upper bounds regarding the maximum number of equiangular lines in
dimensions d=14, and d=16. Additionally, we prove the nonexistence of certain
regular graphs with four eigenvalues, and correct some tables from the
literature.Comment: 24 pages, to appear in JCTA. Corrected an entry in Table
Some Implications on Amorphic Association Schemes
AMS classifications: 05E30, 05B20;amorphic association scheme;strongly regular graph;(negative) Latin square type;cyclotomic association scheme;strongly regular decomposition