Transactions on Combinatorics, Year (2019-10)

Title : ( Bounds for metric dimension and defensive k-alliance of graphs under deleted lexicographic product )

Authors: KINKAR CHANDRA DAS , Mostafa Tavakoli ,

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Abstract

Metric dimension and defensive k-alliance number are two distance-based graph invari- ants 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.

Keywords

, Deleted lexicographic product, Metric dimension, Defensive k-alliance.