University of Guilan Journal of Algebra and Related Topics 2345-3931 10 2 2022 12 01 Three Bounds For Identifying Code Number 61 67 6001 10.22124/jart.2022.20661.1321 EN E. Vatandoost Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. K. Mirasheh Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. Journal Article 2021 09 21 Let $G=(V, E)$ be a simple graph. A set $C$ of vertices $G$ is an identifying set of $G$ if for every two vertices $x$ and $y$ belong to $V$ 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 set of $G$ is called the identifying code number of $G$ and is denoted by $\gamma^{ID}(G).$ Two vertices $x$ and $y$ are twins when $N_{G}[x]=N_{G}[y].$ Graphs with at least two twin vertices are not identifiable graphs. In this paper,  we present three bounds for identifying code number. https://jart.guilan.ac.ir/article_6001_d947a6fc079678e48603d4bbcb973754.pdf