کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4648187 1342397 2012 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The metric dimension of the lexicographic product of graphs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
The metric dimension of the lexicographic product of graphs
چکیده انگلیسی

For a set WW of vertices and a vertex vv in a connected graph GG, the kk-vector rW(v)=(d(v,w1),…,d(v,wk))rW(v)=(d(v,w1),…,d(v,wk)) is the metric representation   of vv with respect to WW, where W={w1,…,wk}W={w1,…,wk} and d(x,y)d(x,y) is the distance between the vertices xx and yy. The set WW is a resolving set   for GG if distinct vertices of GG have distinct metric representations with respect to WW. The minimum cardinality of a resolving set for GG is its metric dimension  . In this paper, we study the metric dimension of the lexicographic product of graphs GG and HH, denoted by G[H]G[H]. First, we introduce a new parameter, the adjacency dimension  , of a graph. Then we obtain the metric dimension of G[H]G[H] in terms of the order of GG and the adjacency dimension of HH.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 312, Issue 22, 28 November 2012, Pages 3349–3356
نویسندگان
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