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Published in:
2024 | OriginalPaper | Chapter
On the Minimum Locating Number of Graphs with a Given Order
Authors : Sul-young Choi, Puhua Guan
Published in: Combinatorics, Graph Theory and Computing
Publisher: Springer Nature Switzerland
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Abstract
A locating set S in a connected graph is a set of vertices satisfying that \(N(u)\cap S\) is unique for each vertex u not in S. A locating set can be considered as a set of sensors which can determine the exact location of an intruder. The size of a smallest locating set of a graph G is called the locating number of the graph and denoted by \(ln(G)\). We show that \(min\, \{ln(G): G \) is a connected graph with n vertices \(\} = s\) when \(2^{s-1}+(s-1) < n \leq 2^s+s\).
