اخبار و اعلانات

 آمار

تعداد نشریات44
تعداد شماره‌ها1,877
تعداد مقالات15,278
تعداد مشاهده مقاله43,730,724
تعداد دریافت فایل اصل مقاله17,563,037
Roozbayani, Maryam, Maimani, Hamidreza, Tehranian, Abolfazl. (1392). Watching systems of triangular graphs. , 3(1), 51-57. doi: 10.22108/toc.2014.4127
Maryam Roozbayani; Hamidreza Maimani; Abolfazl Tehranian. "Watching systems of triangular graphs". , 3, 1, 1392, 51-57. doi: 10.22108/toc.2014.4127
Roozbayani, Maryam, Maimani, Hamidreza, Tehranian, Abolfazl. (1392). 'Watching systems of triangular graphs', , 3(1), pp. 51-57. doi: 10.22108/toc.2014.4127
Roozbayani, Maryam, Maimani, Hamidreza, Tehranian, Abolfazl. Watching systems of triangular graphs. , 1392; 3(1): 51-57. doi: 10.22108/toc.2014.4127

Watching systems of triangular graphs

Transactions on Combinatorics
مقاله 6، دوره 3، شماره 1، خرداد 2014، صفحه 51-57    اصل مقاله (302.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2014.4127
نویسندگان
Maryam Roozbayani1؛ Hamidreza Maimani* 2؛ Abolfazl Tehranian1
1Science and Research Branch, Islamic Azad University
2Shahid Rajaee Teacher Training University
چکیده
A watching system in a graph $G=(V‎, ‎E)$ is a set $W=\{\omega_{1}‎, ‎\omega_{2}‎, ‎\dots‎, ‎\omega_{k}\}$‎, ‎where $\omega_{i}=(v_{i}‎, ‎Z_{i})‎, ‎v_{i}\in V$ and $Z_{i}$ is a subset of closed neighborhood of‎ ‎$v_{i}$ such that the sets $L_{W}(v)=\{\omega_{i}‎: ‎v\in‎ ‎Z_{i}\}$ are non-empty and distinct‎, ‎for any $v\in V$‎. ‎In this‎ ‎paper‎, ‎we study the watching systems of line graph $K_{n}$ which is‎ ‎called triangular graph and denoted by $T(n)$‎. ‎The minimum size of a‎ ‎watching system of $G$ is denoted by $\omega(G)$‎. ‎We show that‎ ‎$\omega(T(n))=\lceil\frac{2n}{3}\rceil$‎.
کلیدواژه‌ها
Identifying code؛ Watching system؛ Triangular graph
مراجع
D. Auger (2010) Minimal identifying codes in trees and planar graphs with large girth European J. Combin. 31 (5), 1372-1384
D. Auger, I. Charon, O. Hurdy and A. Lobstein (2013) Watching systems in graphs: an extension of identifying codes Discrete Appl. Math. 161 (12), 1674-1685
I. Charon, O. Hudry and A. Lobstein (2003) Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard Theoret. Comput. Sci. 290 (3), 2109-2120
I. Charon, O. Hudry and A. Lobstein (2007) Extremal cardinalities for identifying and locating-dominating codes in graphs Discrete Math. 307 (3-5), 356-366
R. Diestel (1997) Graph theory Translated from the 1996 German original, Graduate Texts in Mathematics, Springer-Verlag, New York 173
M. G. Karpovsky, K. Chakrabarty and L. B. Levitin (1998) On a new class of codes for identifying vertices in graphs IEEE Trans. Inform. Theory 44, 599-611
F. Foucaud, E. Guerrini, M. Kovse, R. Naserasr, A. Parreau and P. Valicov (2011) Extremal graphs for the identifying code problem European J. Combin. 32 (4), 628-638
F. Foucauda, S. Gravierb, R. Naserasra, A. Parreaub and P. Valicova (2013) Identifying codes in line graphs J. Graph Theory 37 (4), 425-448
F. Foucaud, R. Klasing, A. Kosowski and A. Raspaud (2012) On the size of identifying codes in triangle-free graphs Discrete Appl. Math. 160 (10-11), 1532-1546
آمار
تعداد مشاهده مقاله: 4,500
تعداد دریافت فایل اصل مقاله: 3,178


سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب