key distribution is an important problem in wireless sensor networks where sensor nodesare randomly scattered in adversarial environments.due to the random deployment of sensors, a list of keys must be pre-distributed to each sensor node before deployment. to establish a secure communication, two nodes must share common key from their key-rings. otherwise, they can find a key- path in which ens...

In this paper, we study when the incidence matrix of a symmetric (v, k, λ)-BIBD is a 3-frameproof code. We show the existence of infinite families of symmetric BIBDs that are 3-frameproof codes, as well as infinite families of symmetric BIBDs that are not 3-frameproof codes.

1. Introduction In this paper we consider some results on the orbits of groups of collineations, or, more generally, on the point and block classes of tactical decompositions, on symmetric balanced incomplete block designs (symmetric BIBD = (v, k, 2)-system=finite 2-plane), and we consider generalizations to (not necessarily symmetric) BIBD and other combinatorial designs. The results are about...

Using Lagrange’s multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.  2003 E...

"We investigateof the all-ones matrix .]V for1) 16 over va,rious admissible groups. For 1) 16 allhave been PIlumera,ted. For the case 7) 16 only some classes have been completely enumerated. Of particularare signings over the group since these can alsobe considHed as GDD(16 X 2,16,these overexpanding,GDD(16 4,16,4)'s. We continne in this way until we obtainG ...

Given a BIBD(v,k,A) we can construct a directed BIBD(v,k,A*) by writing each block of the BIBO twice, the second time in the reversed order. Here we prove the analagous expected but useful result that if a BIBD(v,b,r ks,k,A) exists, then a RCOBIBD(v,k,A *} also exists. A nonexistence result is also given.

Definition: Let v, k, and λ be positive integers such that v > k ≥ 2. A (v, k, λ)-balanced incomplete block design (which we abbreviate to (v, k, λ)-BIBD) is a design (X,A) such that the following properties are satisfied: 1. |X| = v, 2. Each block contains exactly k points, and 3. Every pair of distinct points is contained in exactly λ blocks. Property 3 in the definition above is the “balance...

Balanced incomplete-block designs (BIBDs) with repeated blocks are studied and constructed. We continue work initiated by van Lint and Ryser in 1972 and pursued by van Lint in 1973. We concentrate on constructing (v, b, r, k, λ)-BIBDs with repeated blocks, especially those with gcd(b, r, λ) = 1 and r ≤ 20. We obtain new bounds for the multiplicity of a block in terms of the parameters of a BIBD...

When the necessary conditions for a BIBD are satisfied, but no BIBD exists, there is no simple answer for the optimal design problem. This paper identifies the E-optimal information matrices for any such irregular BIBD setting when the number of treatments is no larger than 100. Aand D-optimal designs are typically not E-optimal. An E-optimal design for 15 treatments in 21 blocks of size 5 is f...