Exploring the watching system of polyhedral graphs

Document Type : Full Length Article

Author

Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I. R. Iran

Abstract

Watching system in a graph $G$ is a finite set $W = {w_1, w_2, ..., w_k}$ where each $w_i$ is a couple $w_i = (v_i, Z_i)$, where $v_i$ is a vertex and $Z_i \subset N_G[v_i]$ such that ${Z_1, ..., Z_k}$ is an identifying system.The concept of watching system was first introduced by Auger in [1]. and this system provide an extension of identifying code in the sense that an identifying code is a particular watching system. In this paper, we determine the watching system of specific graphs.

Graphical Abstract

Exploring the watching system of polyhedral graphs

Keywords

Main Subjects


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Volume 9, Issue 2
June 2024
Pages 113-121
  • Receive Date: 05 August 2024
  • Revise Date: 13 August 2024
  • Accept Date: 13 August 2024
  • First Publish Date: 13 August 2024
  • Publish Date: 01 June 2024