Transactions on Combinatorics (Mar 2020)

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

  • Kinkar Chandra Das,
  • Mostafa Tavakoli

DOI
https://doi.org/10.22108/toc.2019.115674.1622
Journal volume & issue
Vol. 9, no. 1
pp. 31 – 39

Abstract

Read online

‎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.

Keywords