A characterization of graphs with upper locating-domination number equal to n-۲

A set D of vertices in a graph G is called a dominating set of G if every vertex in V\left( G\right) \backslash D has at least one neighbor in D. A dominating set D of G is called a locating-dominating set of G if every two vertices in V\left( G\right) \backslash D have two distinct neighborhood sets. The upper locating-domination number \Gamma_{L}(G) is the maximum cardinality of a minimal locating-dominating set of G. In this paper, we characterize the graphs with \Gamma_{L}\left( G\right) =n-۲.

کلیدواژه ها:

dominating set ، locating-dominating set ، upper locating-domination number