%0 Journal Article
%T Different-Distance Sets in a Graph
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Hedetniemi, Jason T.
%A Hedetniemi, Stephen T.
%A Renu C. Laskar, Renu C.
%A Mulder, Henry Martyn
%D 2019
%\ 12/01/2019
%V 4
%N 2
%P 151-171
%! Different-Distance Sets in a Graph
%K Different-Distance Sets
%K Cartesian products
%K graph
%R 10.22049/cco.2019.26467.1115
%X A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$. The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set. We prove that a different-distance set induces either a special type of path or an independent set. We present properties of different-distance sets, and consider the different-istance numbers of paths, cycles, Cartesian products of bipartite graphs, and Cartesian products of complete graphs. We conclude with some open problems and questions.
%U http://comb-opt.azaruniv.ac.ir/article_13863_aa060ff2474ed162917d785d51209d3c.pdf