Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 7 1 2026 02 01 Identifying code number of some of the middle graphs 25 34 240124 10.30504/jims.2026.538124.1271 EN H. Nadimi Dafrazi Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34148-96818, Qazvin, Iran. E. Vatandoost Department of Mathematics‎, ‎Faculty of Science, Imam Khomeini International University‎, ‎P‎.O‎. ‎Box 3414896818‎, ‎Qazvin‎, ‎Iran. Journal Article 2025 07 30 Let $G=(V‎, ‎E)$ be a simple graph‎. ‎A subset $C$ 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 distinct and non-empty‎. ‎Given a graph $G,$ the smallest size of an identifying code of $G$ is called the identifying code number of $G$ and is denoted by $\gamma^{ID}(G).$ In this paper‎, ‎we show that for every graph $G,$ the middle graph of $G$ is an identifiable graph‎. ‎We prove that the identifying code number of the middle graph of $G$ is at most $|V(G)|$‎. ‎Also‎, ‎we determine the identifying code number of the middle graph of some graphs‎. ‎In particular‎, ‎we determine the identifying code number of the middle graph of a bipartite graph‎. https://jims.ims.ir/article_240124_d45b88cf3ca438bbd0cb9446059a3483.pdf