کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4949474 1440190 2017 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The number of completely different optimal identifying codes in the infinite square grid
ترجمه فارسی عنوان
تعداد کدهای شناسایی بهینه کاملا متفاوت در شبکه مربع بی نهایت
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
چکیده انگلیسی
Let G be a graph with vertex set V and edge set E. We call any subset C⊆V an identifying code if the sets I(v)={c∈C|{c,v}∈E or c=v}are distinct and non-empty for all vertices v∈V. We study identifying codes in the infinite square grid. The vertex set of this graph is Z2 and two vertices are connected by an edge if the Euclidean distance between these vertices is one. Ben-Haim & Litsyn have proved that the minimum density of identifying code in the infinite square grid is 720. Such codes are called optimal. We study the number of completely different optimal identifying codes in the infinite square grid. Two codes are called completely different if there exists an integer n such that no n×n-square of one code is equivalent with any n×n-square of the other code. In particular, we show that there are exactly two completely different optimal periodic codes and no optimal identifying code is completely different with both of these two periodic codes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 233, 31 December 2017, Pages 143-158
نویسندگان
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