N. Soltankhah
Department of Mathematics, Alzahra University, P.O. Box 19834, Tehran, Iran.
[ 1 ] - Total perfect codes, OO-irredundant and total subdivision in graphs
Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, ...
[ 2 ] - On the possible volume of $mu$-$(v,k,t)$ trades
A $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$ disjoint collections $T_1$, $T_2, dots T_{mu}$, 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 in each $T_i (1leq i leq mu)$. In other words any pair of collections ${T_i,T_j}$, $1leq i< j leq mu$ is a $(v,k,t)$ trade of volume $m$. In th...
[ 3 ] - On the Volume of µ-way G-trade
A $ mu $-way $ G $-trade ($ mu geq 2) $ consists of $ mu $ disjoint decompositions of some simple (underlying) graph $ H $ into copies of a graph $ G. $ The number of copies of the graph $ G $ in each of the decompositions is the volume of the $ G $-trade and denoted by $ s. $ In this paper, we determine all values $ s $ for which there exists a $ mu $-way $ K_{1,m} $-trade of vo...
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