Bounds for metric dimension and defensive $k$-alliance of graphs under deleted lexicographic product

Document Type: Research Paper


1 Sungkyunkwan University

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad


‎Metric dimension and defensive $k$-alliance number are two distance-based graph invariants‎ ‎which have applications in robot navigation‎, ‎quantitative analysis of secondary RNA structures‎, ‎national defense and fault-tolerant computing‎. ‎In this paper‎, ‎some bounds for metric‎ ‎dimension and defensive $k$-alliance of deleted lexicographic product of graphs are presented‎. ‎We also show that the bounds are sharp‎.