TY - JOUR
ID - 13863
TI - Different-Distance Sets in a Graph
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Hedetniemi, Jason T.
AU - Hedetniemi, Stephen T.
AU - Renu C. Laskar, Renu C.
AU - Mulder, Henry Martyn
AD - Wingate University
AD - Department of Mathematics,
University of Johannesburg,
Auckland Park, South Africa
AD - Clemson University
AD - Erasmus Universiteit
Y1 - 2019
PY - 2019
VL - 4
IS - 2
SP - 151
EP - 171
KW - Different-Distance Sets
KW - Cartesian products
KW - graph
DO - 10.22049/cco.2019.26467.1115
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13863.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13863_aa060ff2474ed162917d785d51209d3c.pdf
ER -