Error-detecting locating dominating sets of Mycielskian of a graph
Abstract
A locating dominating set S is a subset of vertices representing “detectors” in graph G which locate an “intruder.” To precisely locate an intruderin the system, we will place detection devices at a set S of locating dominating vertices in G. The fault-tolerant variant of locating dominating sets is called error-detecting locating dominating sets (DET:LD), where thesystem has at most one false-negative. In this paper, we obtained an upperbound for the error-detecting locating domination number of the generalized Mycielskian of graphs and characterized graphs whose Mycielskian has error-detecting locating domination number 2n, where n is the order of the graph.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Complexity and Algorithms in Graphs
Publication details
- Journal / source
- Proyecciones (Antofagasta)
- Volume
- 44
- Issue
- 4
- Pages
- 702–723
- Publication date
- 16 February 2026
- Language
- EN