کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4949614 1440197 2017 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Trees with equal total domination and game total domination numbers
ترجمه فارسی عنوان
درختان با سلطه برابر و کل سلطه سلطنتی بازی
کلمات کلیدی
بازی سلطه کامل، بازی کل سلطه، درختان،
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
چکیده انگلیسی
In this paper, we continue the study of the total domination game in graphs introduced in Henning et al. (2015), where the players Dominator and Staller alternately select vertices of G. Each vertex chosen must strictly increase the number of vertices totally dominated, where a vertex totally dominates another vertex if they are neighbors. This process eventually produces a total dominating set S of G in which every vertex is totally dominated by a vertex in S. Dominator wishes to minimize the number of vertices chosen, while Staller wishes to maximize it. The game total domination number, γtg(G), (respectively, Staller-start game total domination number, γtg′(G)) of G is the number of vertices chosen when Dominator (respectively, Staller) starts the game and both players play optimally. For general graphs G, sometimes γtg(G)>γtg′(G). We show that if G is a forest with no isolated vertex, then γtg(G)≤γtg′(G). Using this result, we characterize the trees with equal total domination and game total domination number.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 226, 31 July 2017, Pages 58-70
نویسندگان
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