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Exploring the watching system of polyhedral graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 9، شماره 2، شهریور 2024، صفحه 113-121 اصل مقاله (540.3 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11136.1077 | ||
| نویسنده | ||
| Sheyda Maddah* | ||
| Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I. R. Iran | ||
| تاریخ دریافت: 15 مرداد 1403، تاریخ بازنگری: 23 مرداد 1403، تاریخ پذیرش: 23 مرداد 1403 | ||
| چکیده | ||
| Watching system in a graph $G$ is a finite set $W = {w_1, w_2, ..., w_k}$ where each $w_i$ is a couple $w_i = (v_i, Z_i)$, where $v_i$ is a vertex and $Z_i \subset N_G[v_i]$ such that ${Z_1, ..., Z_k}$ is an identifying system.The concept of watching system was first introduced by Auger in [1]. and this system provide an extension of identifying code in the sense that an identifying code is a particular watching system. In this paper, we determine the watching system of specific graphs. | ||
| کلیدواژهها | ||
| watching systems؛ generelized Peteersen graph؛ identifying codes | ||
| مراجع | ||
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[1] D. Auger, I. Charon, O. Hudry, A. Lobstein, Maximum size of a minimum watching system and the graphs achieving the bound, Disc. Appl. Math. 164 (2014) 20–33 [2] D. Auger, I. Charon, O. Hurdy and A. Lobstein, Watching systems in graphs: an extension of identifying codes, Disc. Appl. Math. 161 (2013) 1674–1685. [3] M. Ghorbani, M. Dehmer, H. Maimani, S. Maddah, M. Roozbayani, F. Emmert-Streib, The watching system as a generalization of identifying code, Appl. Math. and Comp. 380 (2020) 125302. [4] S. Maddah, M. Ghorbani, On the watching number of graphs using discharging procedure, Jur. of Appl. Math. and Comp. (2021) 1–12. [5] S. Maddah, M. Ghorbani, M. Dehmer, New results of identifying codes in product graphs, Appl. Math. and Comp. 410 (2021) 126438. | ||
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