In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions given by Feng and Xiang [10, 12]. Three infinite families of strongly regular graphs with new parameters are obtained. The main tools that we employed are i...

The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we investigate the categori...

One approach to supply chain coordination is early order commitment, whereby a retailer commits to purchase a fixedorder quantity at a fixed delivery time before demand uncertainty is resolved. In this paper, we develop an analytical model to quantify the cost savings of an early order commitment in a two-level supply chain where demand is serially correlated. A decision rule is derived to dete...

Relations between Laplacian eigenvectors and eigenvalues and the existence of almost equitable partitions (which are generalizations of equitable partitions) are presented. Furthermore, on the basis of some properties of the adjacency eigenvectors of a graph, a necessary and sufficient condition for the graph to be primitive strongly regular is introduced. c © 2006 Elsevier Ltd. All rights rese...

Wepropose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set ...

We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors’ opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updat...

This note presents an implicit function theorem for generalized equations, simultaneously generalizing Robinson’s implicit function theorem for strongly regular generalized equations and Clarke’s implicit function theorem for equations with Lipschitz-continuous mappings.

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

We provide a new construction of the strongly regular graphs associated with the two sporadic simple groups M22 and HS. Further, we give some new constructions of other known strongly regular graphs by taking the orbits of a certain subgroup of M22 on the planes of the Hermitian variety H(5, 4). These geometric constructions can be used to produce cap codes with large parameters and automorphis...

For every n positive integer we show the construction of a strongly regular graph of order at most 2 which contains every graph of ordered n as a subgraph. The estimation concerning the construction is best possible.