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Mirasheh, Kamran, Abbasi, Ahmad, Vatandoost, Ebrahim. (1404). Proof of a conjecture for the identifying codenumber of the subdivision of graphs. , (), -. doi: 10.22108/toc.2025.143773.2228
Kamran Mirasheh; Ahmad Abbasi; Ebrahim Vatandoost. "Proof of a conjecture for the identifying codenumber of the subdivision of graphs". , , , 1404, -. doi: 10.22108/toc.2025.143773.2228
Mirasheh, Kamran, Abbasi, Ahmad, Vatandoost, Ebrahim. (1404). 'Proof of a conjecture for the identifying codenumber of the subdivision of graphs', , (), pp. -. doi: 10.22108/toc.2025.143773.2228
Mirasheh, Kamran, Abbasi, Ahmad, Vatandoost, Ebrahim. Proof of a conjecture for the identifying codenumber of the subdivision of graphs. , 1404; (): -. doi: 10.22108/toc.2025.143773.2228

Proof of a conjecture for the identifying codenumber of the subdivision of graphs

Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 20 آبان 1404    اصل مقاله (426.38 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.143773.2228
نویسندگان
Kamran Mirasheh* 1؛ Ahmad Abbasi1؛ Ebrahim Vatandoost2
1Department of Pure Mathematics Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-19141, Rasht, Iran
2Department of Basic Science, Imam Khomeini International University, P. O. Box 34148-96818, Qazvin, Iran
چکیده
In this paper, it is proved that the identifying code number of the subdivision graph of $G$ is $n$ where $ |V(G)|=n. $
This result proves the conjecture posed in [S. Ahmadi, E. Vatandoost and A. Behtoie, Domination number and identifying code number of the subdivision graphs, J. Algebr. Syst., 13 no. 2 (2025) pp. 1--11].
کلیدواژه‌ها
Identifying code؛ dominating set؛ subdivision
مراجع

[1] S. Ahmadi, E. Vatandoost and A. Behtoie, Domination number and identifying code number of the subdivision graphs, J. Algebr. Syst., 13 no. 2 (2025) 1–11
[2] F. Foucaud, S. Gravier, R. Naserasr, A. Parreau and P. Valicov, Identifying codes in line graphs, J. Graph Theory, 73 no. 4 (2013) 425–448.
[3] F. Foucaud and G. Perarnau, Bounds for identifying codes in terms of degree parameters, Electron. J. Combin., 19 no. 1 (2012) Paper 32, 28 pp.
[4] O. Hudry and A. Lobstein, Unique (optimal) solutions: complexity results for identifying and locating-dominating codes, Theoret. Comput. Sci., 767 (2019) 83–102.
[5] M. Roozbayani and H. R. Maimani, Identifying codes and watching systems in Kneser graphs, Discrete Math. Algorithms Appl., 9 no. 1 (2017) 9 pp.
[6] D. F. Rall and K. Wash, Identifying codes of the direct product of two cliques, European J. Combin., 36 (2014) 159–171.
[7] A. Shaminejad, E. Vatandoost and K. Mirasheh, The identifying code number and Mycielski’s construction of graphs, Trans. Comb., 11 no. 4 (2022) 309–316.

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