Transactions on Combinatorics (Mar 2020)
Bounds for metric dimension and defensive $k$-alliance of graphs under deleted lexicographic product
Abstract
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.
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