Exploring the watching system of polyhedral graphs

Maddah, Sheyda

doi:10.22061/jdma.2024.11136.1077

Exploring the watching system of polyhedral graphs

Document Type : Full Length Article

Author

Sheyda Maddah

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

10.22061/jdma.2024.11136.1077

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 graphs.

Graphical Abstract