Let $G=(V, E)$ be a simple graph. A set $C$ of vertices of $G$ is an identifying code of $G$ if for every two vertices $x$ and $y$ the sets $N_{G}[x] \cap C$ and $N_{G}[y] \cap C$ are non-empty and different. Given a graph $G,$ the smallest size of an identifying code of $G$ is called the identifying code number of $G$ and denoted by $\gamma^{ID}(G).$ In this paper, we prove that the identifying code number of the subdivision of a graph $G$ of order $n$ is at most $n$. Also, we prove that the identifying code number of the subdivision of graphs $K_n$, $K_{r,s}$ and $C_P(s)$ are $n$, $r+s$ and $2s$, respectively. Finally, we conjecture that for every graph $G$ of order $n$ the identifying code number of the subdivision of $G$ is $n$.
Behtoei, A., Ahmadi, S., & Vatandoost, E. (2024). Domination Number and Identifying Code Number of the Subdivision Graphs. Journal of Algebraic Systems, (), -. doi: 10.22044/jas.2023.12257.1649
MLA
Ali Behtoei; Somaiya Ahmadi; Ebrahim Vatandoost. "Domination Number and Identifying Code Number of the Subdivision Graphs". Journal of Algebraic Systems, , , 2024, -. doi: 10.22044/jas.2023.12257.1649
HARVARD
Behtoei, A., Ahmadi, S., Vatandoost, E. (2024). 'Domination Number and Identifying Code Number of the Subdivision Graphs', Journal of Algebraic Systems, (), pp. -. doi: 10.22044/jas.2023.12257.1649
VANCOUVER
Behtoei, A., Ahmadi, S., Vatandoost, E. Domination Number and Identifying Code Number of the Subdivision Graphs. Journal of Algebraic Systems, 2024; (): -. doi: 10.22044/jas.2023.12257.1649
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