Identifying code number of some of the middle graphs
نویسندگان
1 Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34148-96818, Qazvin, Iran.
2 Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 3414896818, Qazvin, Iran.
doi
10.30504/jims.2026.538124.1271چکیده
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.
