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Different-Distance Sets in a Graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 4، شماره 2، زمستان 2019، صفحه 151-171 اصل مقاله (586.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26467.1115 | ||
| نویسندگان | ||
Jason T. Hedetniemi  1؛ Stephen T. Hedetniemi2؛ Renu C. Renu C. Laskar3؛ Henry Martyn Mulder 4
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| 1Wingate University | ||
| 2Department of Mathematics, University of Johannesburg, Auckland Park, South Africa | ||
| 3Clemson University | ||
| 4Erasmus Universiteit | ||
| چکیده | ||
| 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-distance numbers of paths, cycles, Cartesian products of bipartite graphs, and Cartesian products of complete graphs. We conclude with some open problems and questions. | ||
| کلیدواژهها | ||
| Di fferent-Distance Sets؛ Cartesian products؛ graph | ||
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آمار تعداد مشاهده مقاله: 370 تعداد دریافت فایل اصل مقاله: 242 |
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