The Simultaneous Metric Dimension of Families Composed by Lexicographic Product Graphs
نویسندگان
چکیده
منابع مشابه
The metric dimension of the lexicographic product of graphs
A set of vertices W resolves a graph G if every vertex is uniquely determined by its coordinate of distances to the vertices in W . The minimum cardinality of a resolving set of G is called themetric dimension of G. In this paper, we consider a graphwhich is obtained by the lexicographic product between two graphs. The lexicographic product of graphs G and H , which is denoted by G ◦ H , is the...
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A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
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The concept of (minimum) resolving set has proved to be useful and/or related to a variety of fields such as Chemistry [3,6], Robotic Navigation [5,8] and Combinatorial Search and Optimization [7]. This work is devoted to evaluating the so-called metric dimension of a finite connected graph, i.e., the minimum cardinality of a resolving set, for a number of graph families, as long as to study it...
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For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d(v, w1), d(v, w2), . . . , d(v, wk)) is called the (metric) representation of v with respect to W , where d(x, y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respe...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2016
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-016-1675-1