Identifying codes and watching systems in Kneser graphs-Reference-Cited by-同舟云学术

Identifying codes and watching systems in Kneser graphs

Published:2017-02 Issue:01 Volume:09 Page:1750007
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Roozbayani Maryam¹,Maimani Hamid Reza²³

Affiliation:

1. Department of Mathematics, Science and Research Branch, Islamic, Azad University, Tehran, Iran

2. Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P. O. Box 16785-163, Tehran, Iran

3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

Abstract

Identifying code in graph [Formula: see text] is a subset [Formula: see text] of [Formula: see text] such that [Formula: see text] for every [Formula: see text] of [Formula: see text] and [Formula: see text] for every [Formula: see text] of [Formula: see text]. The minimum size of identifying codes of graph [Formula: see text] is denoted by [Formula: see text]. A watching system in a graph [Formula: see text] is a set [Formula: see text], where [Formula: see text] and [Formula: see text] is a subset of closed neighborhood of [Formula: see text] such that the sets [Formula: see text] are nonempty and distinct, for any [Formula: see text]. The minimum size of a watching system of [Formula: see text] is denoted by [Formula: see text]. In this paper, we show if [Formula: see text], then [Formula: see text] if [Formula: see text] (mod 3) and [Formula: see text] if [Formula: see text] (mod 3). Also we show that [Formula: see text]. This means that in this family of graphs the watching system is more efficient than identifying code.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830917500070

Reference10 articles.

1. Minimal identifying codes in trees and planar graphs with large girth

2. Watching systems in graphs: An extension of identifying codes

3. Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard

4. Extremal cardinalities for identifying and locating-dominating codes in graphs

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