MINIMAL DOUBLY RESOLVING SETS AND THE STRONG METRIC DIMENSION OF HAMMING GRAPHS

被引：41

作者：

Kratica, Jozef ^{[1
]}

Kovacevic-Vujcic, Vera ^{[2
]}

Cangalovic, Mirjana ^{[2
]}

Stojanovic, Milica ^{[2
]}

机构：

[1] Serbian Acad Arts & Sci, Math Inst, Belgrade 11000, Serbia

[2] Univ Belgrade, Fac Org Sci, Belgrade 11000, Serbia

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2012年 / 6卷 / 01期

关键词：

Hamming graphs; metric dimension; minimal doubly resolving set; strong metric dimension; graph theory; DIGRAPHS;

D O I：

10.2298/AADM111116023K

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of determining the carclinality psi(H-2,H-k) of minimal doubly resolving sets of Hamming graphs H-2,H-k. We prove that for k >= 6 every minimal resolving set of H-2,H-k is also a doubly resolving set, and, consequently psi(H-2,H-k) is equal to the metric dimension of H-2,H-k, which is known from the literature. Moreover, we find an explicit expression for the strong metric dimension of all Hamming graphs H-n,H-k.

引用

页码：63 / 71

页数：9

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