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Dehgardai, Nasrin, Norouzian, Sepideh, Sheikholeslami, Seyed Mahmoud. (1391). Bounding the domination number of a tree in terms of its annihilation number. , 2(1), 9-16. doi: 10.22108/toc.2013.2652
Nasrin Dehgardai; Sepideh Norouzian; Seyed Mahmoud Sheikholeslami. "Bounding the domination number of a tree in terms of its annihilation number". , 2, 1, 1391, 9-16. doi: 10.22108/toc.2013.2652
Dehgardai, Nasrin, Norouzian, Sepideh, Sheikholeslami, Seyed Mahmoud. (1391). 'Bounding the domination number of a tree in terms of its annihilation number', , 2(1), pp. 9-16. doi: 10.22108/toc.2013.2652
Dehgardai, Nasrin, Norouzian, Sepideh, Sheikholeslami, Seyed Mahmoud. Bounding the domination number of a tree in terms of its annihilation number. , 1391; 2(1): 9-16. doi: 10.22108/toc.2013.2652

Bounding the domination number of a tree in terms of its annihilation number

Transactions on Combinatorics
مقاله 1، دوره 2، شماره 1، خرداد 2013، صفحه 9-16    اصل مقاله (443.85 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2013.2652
نویسندگان
Nasrin Dehgardai1؛ Sepideh Norouzian1؛ Seyed Mahmoud Sheikholeslami* 2
1Azarbaijan Shahid Madani University
2Azarbaijan University of Tarbiat Moallem
چکیده
A set $S$ of vertices in a graph $G$ is a dominating set if every‎ ‎vertex of $V-S$ is adjacent to some vertex in $S$‎. ‎The domination‎ ‎number $\gamma(G)$ is the minimum cardinality of a dominating set‎ ‎in $G$‎. ‎The annihilation number $a(G)$ is the largest integer $k$‎ ‎such that the sum of the first $k$ terms of the non-decreasing‎ ‎degree sequence of $G$ is at most the number of edges in $G$‎. ‎In‎ ‎this paper‎, ‎we show that for any tree $T$ of order $n\ge 2$‎, ‎$\gamma(T)\le \frac{3a(T)+2}{4}$‎, ‎and we characterize the trees‎ ‎achieving this bound‎.
کلیدواژه‌ها
annihilation number؛ dominating set؛ Domination Number
مراجع
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