دانشگاه شهید مدنی آذربایجان

 آمار

تعداد نشریات6
تعداد شماره‌ها131
تعداد مقالات1,634
تعداد مشاهده مقاله1,899,064
تعداد دریافت فایل اصل مقاله1,758,846
Amjadi, J., Ebadi, M., Sheikholeslami, Seyed Mahmoud, Volkmann, L.. (1405). Upper bounds for $[1,2]$-domination number in trees. , 11(4), 1163-1174. doi: 10.22049/cco.2026.31357.2831
J. Amjadi; M. Ebadi; Seyed Mahmoud Sheikholeslami; L. Volkmann. "Upper bounds for $[1,2]$-domination number in trees". , 11, 4, 1405, 1163-1174. doi: 10.22049/cco.2026.31357.2831
Amjadi, J., Ebadi, M., Sheikholeslami, Seyed Mahmoud, Volkmann, L.. (1405). 'Upper bounds for $[1,2]$-domination number in trees', , 11(4), pp. 1163-1174. doi: 10.22049/cco.2026.31357.2831
Amjadi, J., Ebadi, M., Sheikholeslami, Seyed Mahmoud, Volkmann, L.. Upper bounds for $[1,2]$-domination number in trees. , 1405; 11(4): 1163-1174. doi: 10.22049/cco.2026.31357.2831

Upper bounds for $[1,2]$-domination number in trees

Communications in Combinatorics and Optimization
مقاله 9، دوره 11، شماره 4، اسفند 2026، صفحه 1163-1174    اصل مقاله (369.8 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2026.31357.2831
نویسندگان
J. Amjadi* 1؛ M. Ebadi1؛ Seyed Mahmoud Sheikholeslami* 1؛ L. Volkmann2
1Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran
2Institute for Geometry and Practical Mathematics, RWTH Aachen University, 52056 Aachen, Germany
چکیده
A set $S$ of vertices is a $[1,2]$-set of a graph $G$ if every vertex $v$ not in $S$ is adjacent to at least one but no more than two vertices in $S$. The minimum cardinality of a $[1,2]$-set is the $[1,2]$-domination number. In this paper, we present two upper bounds on the $[1,2]$-domination number of trees in terms of the order, number of support vertices and number of leaves. Furthermore, extremal trees reaching one of these two bounds are provided.
کلیدواژه‌ها
$[1,2]$-set؛ $[1,2]$-domination number؛ trees
مراجع
[1] J. Cáceres, C. Hernando, M. Mora, I.M. Pelayo, and M.L. Puertas González, Perfect and quasiperfect domination in trees, Appl. Analysis Discrete Math. 10 (2016), 46–64. https://doi.org/10.2298/AADM160406007C

[2] Y. Caro, A. Hansberg, and M. Henning, Fair domination in graphs, Discrete Math. 312 (2012), 2905–2914. https://doi.org/10.1016/j.disc.2012.05.006

[3] M. Chellali, T.W. Haynes, S.T. Hedetniemi, and A. McRae, $[1, 2]$-sets in graphs, Discrete Appl. Math. 161 (2013), 2885–2893.  https://doi.org/10.1016/j.dam.2013.06.012

[4] M. Livingston and Q.F. Stout, Perfect dominating sets, Congr. Numer. 79 (1990), 187–203.

آمار
تعداد مشاهده مقاله: 349
تعداد دریافت فایل اصل مقاله: 344


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب