Locating dominating codes: Bounds and extremal cardinalities

TL;DR

This paper investigates bounds and extremal sizes of two types of codes in graphs that both dominate and locate vertices, with applications in network detection and system control.

Contribution

It provides new bounds, extremal values, and realization theorems for mbda-codes and ta-codes, advancing understanding of their properties.

Findings

Derived bounds for mbda-codes and ta-codes

Identified extremal cardinalities for these codes

Established realization theorems for code configurations

Abstract

In this work, two types of codes such that they both dominate and locate the vertices of a graph are studied. Those codes might be sets of detectors in a network or processors controlling a system whose set of responses should determine a malfunctioning processor or an intruder. Here, we present our more significant contributions on \lambda-codes and \eta-codes concerning concerning bounds, extremal values and realization theorems.