@article {
author = {Hedetniemi, Jason T. and Hedetniemi, Stephen T. and Renu C. Laskar, Renu C. and Mulder, Henry Martyn},
title = {Different-Distance Sets in a Graph},
journal = {Communications in Combinatorics and Optimization},
volume = {4},
number = {2},
pages = {151-171},
year = {2019},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26467.1115},
abstract = {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.},
keywords = {Different-Distance Sets,Cartesian products,graph},
url = {http://comb-opt.azaruniv.ac.ir/article_13863.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13863_aa060ff2474ed162917d785d51209d3c.pdf}
}