TY - JOUR ID - 778 TI - Total perfect codes‎, ‎OO-irredundant and total subdivision in graphs JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Hosseinzadeh, H. AU - Soltankhah, N. AD - Department of Mathematics‎, ‎Alzahra University‎, ‎P.O. Box 19834, Tehran‎, ‎Iran. AD - Department of Mathematics‎, ‎Alzahra University‎, ‎P.O. Box 19834, Tehran‎, ‎Iran. Y1 - 2016 PY - 2016 VL - 42 IS - 3 SP - 499 EP - 506 KW - Total domination number KW - OO‎- ‎irredundance number‎ KW - total subdivision number DO - N2 - ‎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, we determine the value of $ooir(G)$ for some classes of graphs‎. UR - http://bims.iranjournals.ir/article_778.html L1 - http://bims.iranjournals.ir/article_778_fa2994302d0b573b33b69934d84dde37.pdf ER -