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On the existence of (v, k, t) trades
TLDR
A (v, k, t) trade can be used to construct new designs with various support sizes from a given t-design, where 2t < s < 2t + 2t-l. Expand
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On defining numbers of k-chromatic k-regular graphs
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Smallest defining number of r-regular k-chromatic graphs: r 1 k
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On defining sets of directed designs
TLDR
The concept of defining set has been studied in block designs and, under the name critical sets, in Latin squares and Room squares. Expand
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On directed trades
TLDR
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
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Results on Total Domination and Total Restrained Domination in Grid Graphs
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 restrainedExpand
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On the non-existence of some Steiner $t$-$(v,k)$ trades of certain volumes
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 thatExpand
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Smallest defining sets of super-simple 2 - (v, 4,1) directed designs
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 atExpand
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ON THE POSSIBLE VOLUME OF -( v; k; t ) TRADES
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 sameExpand
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Directed Quadruple Designs
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 ofExpand
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