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- W2804188439 abstract "Let G =( V , E ) be a connected graph and W ={ w 1 , w 2 , …, w k } be an ordered subset of V ( G ). For any vertex v ∈ V , the locating code of v with respect to W is the k -vector C W ( v )={ d ( v , w 1 ), d ( v , w 2 ), …, d ( v , w k )}, W is said to be a locating set of G if distinct vertices have the distinct locating code, and the locating number of G is defined as: Loc ( G )=min{| W |: W is a locating set of G }.We study the locating set and locating number of a graph G , obtain some bounds for the locating numbers of graphs, and determine the exact value of Loc ( G ) for some special classes of graphs, such as cycles, wheels, complete t -partite graph and some Cartesian products of paths and cycles. In addition, we also prove that Loc ( T )≥ Δ -1 holds for all trees T with maximum degree Δ , and shows a tree T with Loc ( T )= Δ -1." @default.
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- W2804188439 date "2018-02-25" @default.
- W2804188439 modified "2023-09-28" @default.
- W2804188439 title "On Locating Numbers of Graphs" @default.
- W2804188439 doi "https://doi.org/10.11916/j.issn.1005-9113.16198" @default.
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