Identifying code number of some Cayley graphs

Document Type : Research Paper

Authors

1 Department of Basic Science, Imam Khomeini International University, P. O. Box 3414896818, Qazvin, Iran

2 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

Let $\Gamma=(V, E)$ be a simple graph. A set $C$ of vertices $\Gamma$ is an identifying  set  of $\Gamma$ if for every two vertices $x$ and $y$ the sets $N_{\Gamma}[x] \cap C$ and $N_{\Gamma}[y] \cap C$ are non-empty and different. Given a graph $\Gamma,$ the smallest size of an identifying set of $\Gamma$ is called the identifying code number of $\Gamma$ and is denoted by $\gamma^{ID}(\Gamma).$ Two vertices $x$ and $y$ are twins when $N_{\Gamma}[x]=N_{\Gamma}[y].$ Graphs with at least two twin vertices are not identifiable graph. In this paper, we study identifying code number of some Cayley graphs.

Keywords

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Volume 13, Issue 2
July 2022
Pages 3183-3189
  • Receive Date: 10 November 2021
  • Revise Date: 20 February 2022
  • Accept Date: 19 May 2022