Resolvability and Strong Resolvability in the Direct Product of Graphs
نویسندگان
چکیده
منابع مشابه
On connected resolvability of graphs
For an ordered set W = {w1, w2, · · · , wk} of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the k-vector r(v|W ) = (d(v, w1), d(v, w2), · · · , d(v, wk)), where d(x, y) represents the distance between the vertices x and y. The set W is a connected resolving set for G if distinct vertices of G have distinct representations with respect to W and the...
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A vertex u in a graph G resolves a pair of distinct vertices x, y of G if the distance between u and x is different from the distance between u and y. A set W of vertices in G resolves the graph G if every pair of distinct vertices of G is resolved by some vertices in W . The metric dimension of a graph, denoted by dim(G), is the smallest cardinality of a resolving set. A resolving set W for a ...
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For an ordered setW = {w1,w2, . . . ,wk} of vertices and a vertexv in a connected graphG, the code of v with respect toW is the k-vector cW (v)= (d(v,w1),d(v,w2), . . . ,d(v,wk)), where d(x,y) represents the distance between the vertices x andy . The setW is a resolving set for G if distinct vertices of G have distinct codes with respect to W . The minimum cardinality of a resolving set for G i...
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2016
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-016-0563-6