دانشگاه شهید مدنی آذربایجان

 آمار

تعداد نشریات7
تعداد شماره‌ها102
تعداد مقالات1,142
تعداد مشاهده مقاله1,049,286
تعداد دریافت فایل اصل مقاله868,730
Hedetniemi, Jason, Hedetniemi, Stephen, Renu C. Laskar, Renu C., Mulder, Henry Martyn. (1399). The 2-dimension of a Tree. , 5(1), 69-81. doi: 10.22049/cco.2019.26495.1119
Jason Hedetniemi; Stephen Hedetniemi; Renu C. Renu C. Laskar; Henry Martyn Mulder. "The 2-dimension of a Tree". , 5, 1, 1399, 69-81. doi: 10.22049/cco.2019.26495.1119
Hedetniemi, Jason, Hedetniemi, Stephen, Renu C. Laskar, Renu C., Mulder, Henry Martyn. (1399). 'The 2-dimension of a Tree', , 5(1), pp. 69-81. doi: 10.22049/cco.2019.26495.1119
Hedetniemi, Jason, Hedetniemi, Stephen, Renu C. Laskar, Renu C., Mulder, Henry Martyn. The 2-dimension of a Tree. , 1399; 5(1): 69-81. doi: 10.22049/cco.2019.26495.1119

The 2-dimension of a Tree

Communications in Combinatorics and Optimization
مقاله 17، دوره 5، شماره 1، شهریور 2020، صفحه 69-81    اصل مقاله (617.73 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2019.26495.1119
نویسندگان
Jason Hedetniemi1؛ Stephen Hedetniemi2؛ Renu C. Renu C. Laskar3؛ Henry Martyn Mulder* 4
1Department of Mathematics Wingate University Wingate NC USA
2School of Computing Clemson University Clemson, SC U.S.A.
3Clemson University
4Econometrisch Instituut Erasmus Universiteit Rotterdam Netherlands
چکیده
Let $x$ and $y$ be two distinct vertices in a connected graph $G$. The $x,y$-location of a vertex $w$ is the ordered pair of distances from $w$ to $x$ and $y$, that is, the ordered pair $(d(x,w), d(y,w))$. A set of vertices $W$ in $G$ is $x,y$-located if any two vertices in $W$ have distinct $x,y$-locations. A set $W$ of vertices in $G$ is 2-located if it is $x,y$-located, for some distinct vertices $x$ and $y$. The 2-dimension of $G$ is the order of a largest set that is 2-located in $G$. Note that this notion is related to the metric dimension of a graph, but not identical to it. We study in depth the trees $T$ that have a 2-locating set, that is, have 2-dimension equal to the order of $T$. Using these results, we have a nice characterization of the 2-dimension of arbitrary trees.
کلیدواژه‌ها
resolvability؛ location number؛ 2-dimension؛ tree؛ 2-locating set
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] F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976), 191–195.

[3] S.T. Hedetniemi, R.C. Laskar, and H.M. Mulder, New resolvability parameters of graphs, submitted.

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

 

آمار
تعداد مشاهده مقاله: 634
تعداد دریافت فایل اصل مقاله: 356


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب