The group PSL(2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all… (More)

Let R be a commutative ring with identity. Let Γ(R) be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if Ra + Rb = R. In this paper we consider a… (More)

Let R be a commutative ring with identity and let I be an ideal of R. Let R 1 I be the subring of R×R consisting of the elements (r,r + i) for r ∈ R and i ∈ I. We study the diameter and girth of the… (More)

A t-(v, k, J\) design D = (X, B) with B = Pk(X) is called a full design. For t = 2, k = 3 and any v, we give minimal defining sets for these designs. For v = 6 and v = 7, smallest defining sets are… (More)

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by Γ(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In… (More)

In this paper, we present a complete classification of the simple 2-(v, 3) trades, for v = 6 and 7. For v = 6, up to isomorphism, there are unique trades with volumes 4, 6, and 10 and trades with… (More)

A set of blocks which is a subset of blocks of only one design is called a defining set of that design. In this paper we determine smallest defining sets of the 21 nonisomorphic 2-(10,5,4) designs.

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R) = A(R)r {0}… (More)