we investigate the existence of some‎ ‎large sets of size nine‎. ‎the large set $ls[9](2,5,29)$ is constructed and‎ ‎existence of the family $ls[9](2,5,27l+j)$ for $lgeq 1, ‎2leq‎ ‎j

Using covering numbers we prove that a standard real integral table algebra (A, B) with |B| ≥ 6 has a P-polynomial structure with respect to every b = 1 in B if and only if 2|B| − 1 is prime and (A, B) is exactly isomorphic to the Bose-Mesner algebra of the association scheme of the ordinary (2|B| − 1)-gon. Then we present an example showing that this result is not true if |B| ≤ 5.

Kramer-Mesner matrices have been used as a powerful tool to construct t-designs. In this paper we construct Kramer-Mesner matrices for xed values of k and t in which the entries are polynomials in n the number of vertices of the underlying graph. From this we obtain an elementary proof that with a few exceptions S 2] n is a maximal subgroup of S (n 2) or A (n 2). We also show that there are onl...

Motivated from an example of ridge graphs relating to metric polytopes, a class of connected regular graphs such that the squares of their adjacency matrices are in certain symmetric Bose-Mesner algebras of dimension 3 is considered in this paper as a generalization of strongly regular graphs. In addition to analysis of this prototype example defined over ðMetP5Þ , some general properties of th...

Suppression on HAART Kathryn Bello, DO; Octavio Mesner, MS; Thomas O’bryan, MD; Tahaniyat Lalani, MBBS, MHS; Anuradha Ganesan, MD; Brian Agan, MD; Jason Okulicz, MD; Internal Medicine, San Antonio Military Medical Center, Fort Sam Houston, TX; Infectious Disease Clinical Research Program, Uniformed Services University of the Health Sciences, Rockville, MD; Infectious Disease Clinical Research P...

Intriguing and tight sets of vertices of point-line geometries have recently been studied in the literature. In this paper, we indicate a more general framework for dealing with these notions. Indeed, we show that some of the results obtained earlier can be generalized to larger classes of graphs. We also give some connections and relations with other notions and results from algebraic graph th...

In this paper, we exploit some intersection matrices to empower a backtracking approach based on Kramer–Mesner matrices. As an application, we consider the interesting family of simple t-ðtþ 8; tþ 2; 4Þ designs, 1 t 4, and provide a complete classification for t 1⁄4 1; 4, as well as a classification of all non-rigid designs for t 1⁄4 2; 3. We also enumerate all rigid designs for t 1⁄4 2. The co...

A subset of the vertex set of a graph G, S ⊆ V (G), is a (k, τ)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has τ neighbors in it. This paper is a contribution to the given problem of existence of (k, τ)-regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose-Mesner algebra of stron...

We give some observations on association schemes with a relation of valency 2 from the representation theory of Bose–Mesner algebras and the basic structure theory. One of the applications of these observations is the classi-cation of the association schemes with a non-symmetric relation of valency 2 if the cardinality of the point set is a product of two primes, and another is the proof of Li’...