Independent locating-dominating sets in some graphs constructed from cycles

Abstract

We investigate independent locating-dominating (ILD) sets in some graph classes constructed from cycles: power of cycles, Möbius ladders, circular ladders, Jahangir graphs, helm graphs and sunflower graphs. These sets are important in applications such as fault detection and monitoring in networks. We demonstrate that power graphs C_n^k with k \geqslant 2 do not admit ILD sets. For the remaining graph families, we establish exact values for the ILD number and present constructive methods for obtaining minimum ILD sets.