پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,307 |
| تعداد دریافت فایل اصل مقاله | 62,488,744 |
Identifying code number of some Cayley graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 255، دوره 13، شماره 2، مهر 2022، صفحه 3183-3189 اصل مقاله (379.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25180.2940 | ||
| نویسندگان | ||
| Somayeh Ahmadi1؛ Ebrahim Vatandoost* 1؛ Ali Bahraini2 | ||
| 1Department of Basic Science, Imam Khomeini International University, P. O. Box 3414896818, Qazvin, Iran | ||
| 2Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| تاریخ دریافت: 19 آبان 1400، تاریخ بازنگری: 01 اسفند 1400، تاریخ پذیرش: 29 اردیبهشت 1401 | ||
| چکیده | ||
| Let $\Gamma=(V, E)$ be a simple graph. A set $C$ of vertices $\Gamma$ is an identifying set of $\Gamma$ if for every two vertices $x$ and $y$ the sets $N_{\Gamma}[x] \cap C$ and $N_{\Gamma}[y] \cap C$ are non-empty and different. Given a graph $\Gamma,$ the smallest size of an identifying set of $\Gamma$ is called the identifying code number of $\Gamma$ and is denoted by $\gamma^{ID}(\Gamma).$ Two vertices $x$ and $y$ are twins when $N_{\Gamma}[x]=N_{\Gamma}[y].$ Graphs with at least two twin vertices are not identifiable graph. In this paper, we study identifying code number of some Cayley graphs. | ||
| کلیدواژهها | ||
| Domination؛ Identifying code؛ Cayley graph | ||
| مراجع | ||
|
[1] D. Auger, Minimal identifying codes in trees and planar graphs with large girth, Eur. J. Combin. 31 (2010), 1372–1384. [2] J. Amjadi, S. Nazari-Moghaddam, S. M. Sheikholeslami and L. Volkmann, Total Roman domination number of trees, Aust. J. Combin. 69 (2017), 271–285. [3] C. Chen, C. Lu and Z. Miao, Identifying codes and locating–dominating sets on paths and cycles, Discrete Appl. Math. 159 (2011), 1540–1547. [4] C. Camarero, C. Martınez and R. Beivide, Identifying codes of degree 4 Cayley graphs over Abelian groups, Adv. Math. Commun. 9 (2015), 129. [5] M. Dettlaff, M. Lemanska, M. Miotk, J. Topp, R. Ziemann and P. Zylinski, Graphs with equal domination and certified domination numbers, Opuscula Math. 39 (2019), 815–827. [6] F. Foucaud, E. Guerrini, M. Kovse, R. Naserasr, A. Parreau and P. Valicov, Extremal graphs for the identifying code problem, Eur. J. Combin. 32 (2011), 628–638. [7] F. Foucaud, R. Klasing, A. Kosowski and A. Raspaud, On the size of identifying codes in triangle-free graphs, Discrete Appl. Math. 160 (2010), 1532–1546. [8] A. Frieze, R. Martin, J. Moncel, M. Ruszinko and C. Smyth, Codes identifying sets of vertices in random networks, Discrete Math. 307 (2007), 1094–1107. [9] S. Gravier, J. Moncel and A. Semri, Identifying codes of cycles, Eur. J. Combin. 27 (2006), 767–776. [10] T. Haynes, D. Knisley, E. Seier and Y. Zou, A quantitative analysis of secondary RNA structure using domination based parameters on trees, BMC Bioinf. 7 (2006), 108. [11] I. Honkala and T. Laihonen, On identifying codes in the triangular and square grids, SIAM J. Comput. 33 (2004), 304–312. [12] M.G. Karpovsky, K. Chakrabarty and L.B. Levitin, On a new class of codes for identifying vertices in graphs, IEEE Trans. Inf. Theory 44 (1998), 599–611. [13] Z. Mansouri and D.A. Mojdeh, Outer independent rainbow dominating functions in graphs, Opuscula Math. 40 (2020), 599–615. [14] R. Nikandish, O. Khani Nasab and E. Dodonge, Minimum identifying codes in some graphs differing by matching, Discrete Math. Algorithms Appl. 12 (2020), 2050046. [15] A. Shaminezhad and E. Vatandoost, On 2-rainbow domination number of functigraph and its complement, Opuscula Math. 40 (2020), 617–627. [16] A. Shaminezhad, E. Vatandoost and K. Mirasheh, The identifying code number and Mycielski’s construction of graphs, Trans. Combin. Articles in press, doi.org/10.22108/TOC.2021.126368.1794. [17] E. Vatandoost and F. Ramezani, On the domination and signed domination numbers of zero-divisor graph, Electron. J. Graph Theory Appl. 4 (2016), 148–156. | ||
|
آمار تعداد مشاهده مقاله: 44,910 تعداد دریافت فایل اصل مقاله: 50,424 |
||