دانشگاه شهید مدنی آذربایجان

 آمار

تعداد نشریات6
تعداد شماره‌ها126
تعداد مقالات1,591
تعداد مشاهده مقاله1,765,707
تعداد دریافت فایل اصل مقاله1,644,428
Hedetniemi, Jason T., Hedetniemi, Stephen T., Renu C. Laskar, Renu C., Mulder, Henry Martyn. (1398). Different-Distance Sets in a Graph. , 4(2), 151-171. doi: 10.22049/cco.2019.26467.1115
Jason T. Hedetniemi; Stephen T. Hedetniemi; Renu C. Renu C. Laskar; Henry Martyn Mulder. "Different-Distance Sets in a Graph". , 4, 2, 1398, 151-171. doi: 10.22049/cco.2019.26467.1115
Hedetniemi, Jason T., Hedetniemi, Stephen T., Renu C. Laskar, Renu C., Mulder, Henry Martyn. (1398). 'Different-Distance Sets in a Graph', , 4(2), pp. 151-171. doi: 10.22049/cco.2019.26467.1115
Hedetniemi, Jason T., Hedetniemi, Stephen T., Renu C. Laskar, Renu C., Mulder, Henry Martyn. Different-Distance Sets in a Graph. , 1398; 4(2): 151-171. doi: 10.22049/cco.2019.26467.1115

Different-Distance Sets in a Graph

Communications in Combinatorics and Optimization
مقاله 8، دوره 4، شماره 2، اسفند 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 Mulder4
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-istance 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
مراجع
[1] G. Chartrand, L. Eroh, M.A. Johnson, and O.R. Oellermann, Resolvability in graphs and the metric dimension of a graph, Discrete Appl. Math. 105 (2000), no. 1-3, 99–113.

[2] G. Chartrand and P. Zhang, The theory and application of resolvability in graphs, Congr. Numer. 160 (2003), 47–68.

[3] R. Hammack, W. Imrich, and S. Klavzar, Handbook of graph products, CRC Press Boca Raton FL, 2011.

[4] H.M. Mulder, The interval function of a graph, Math. Centre Tracts 132, Amsterdam, 1980.

[5] P.J. Slater, Leaves of trees, Congr. Numer. 14 (1975), 549–559.

 

آمار
تعداد مشاهده مقاله: 1,466
تعداد دریافت فایل اصل مقاله: 1,176


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب