A (v, k, t) directed trade of volume s consists of two disjoint collections Tl and each containing ordered k-tuples of distinct elements of a v-set called blocks, such that the number of blocks containing any t-tuple of V is the same in Tl as in T2 .Expand

A set S of vertices in a graph G(V, E) is called a total dominating set if every vertex v ∈ V is adjacent to an element of S. A set S of vertices in a graph G(V, E) is called a total restrained… Expand

Mahmoodian and Soltankhah $\cite{MMS}$ conjectured that there does not exist any $t$-$(v,k)$ trade of volume $s_{i}< s <s_{i+1}$, where $s_{i}=2^{t+1}-2^{t-i}, i=0,1,..., t-1$. Also they showed that… Expand

A $2-(v,k,\lambda)$ directed design (or simply a $2-(v,k,\lambda)DD$) is super-simple if its underlying $2-(v,k,2\lambda)BIBD$ is super-simple, that is, any two blocks of the $BIBD$ intersect in at… Expand

A µ-way (v,k,t) trade of volume m consists of µ disjoint collections T1, T2,...Tµ, each of m blocks, such that for every t-subset of v-set V the number of blocks containing this t-subset is the same… Expand

A t-(v, k, λ) directed design (or simply a t-(v, k, λ)DD) is a pair (V, B), where V is a v-set and B is a collection of ordered k-tuples of distinct elements of V, such that every ordered t-tuple of… Expand