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 = {w1, w2, ..., wk} where each wi is a couple wi = (vi, Zi), where vi is a vertex and Zi ⊆ NG[vi] such that {Z1, ..., Zk} 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 Cayley 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