کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775506 | 1631742 | 2017 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Mixed metric dimension of graphs
ترجمه فارسی عنوان
بعد متریک مختصات نمودارها
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
Let G=(V,E) be a connected graph. A vertex wâ¯ââ¯V distinguishes two elements (vertices or edges) x, yâ¯ââ¯EââªâV if dG(w, x)â¯â â¯dG(w, y). A set S of vertices in a connected graph G is a mixed metric generator for G if every two distinct elements (vertices or edges) of G are distinguished by some vertex of S. The smallest cardinality of a mixed metric generator for G is called the mixed metric dimension and is denoted by dimm(G). In this paper we consider the structure of mixed metric generators and characterize graphs for which the mixed metric dimension equals the trivial lower and upper bounds. We also give results about the mixed metric dimension of some families of graphs and present an upper bound with respect to the girth of a graph. Finally, we prove that the problem of determining the mixed metric dimension of a graph is NP-hard in the general case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 314, 1 December 2017, Pages 429-438
Journal: Applied Mathematics and Computation - Volume 314, 1 December 2017, Pages 429-438
نویسندگان
Aleksander Kelenc, Dorota Kuziak, Andrej Taranenko, Ismael G. Yero,