English

Metric dimension, doubly resolving set and strong metric dimension for $(C_n\Box P_k)\Box P_m$

Combinatorics 2022-08-22 v8

Abstract

A subset Q={q1,q2,...,ql}Q = \{q_1, q_2, ..., q_l\} of vertices of a connected graph GG is a doubly resolving set of GG if for any various vertices x,yV(G)x, y \in V(G) we have r(xQ)r(yQ)λIr(x|Q)-r(y|Q)\neq\lambda I, where λ\lambda is an integer, and II indicates the unit ll- vector (1,...,1)(1,..., 1). A doubly resolving set of vertices of graph GG with the minimum size, is denoted by ψ(G)\psi(G). In this work, we will consider the computational study of some resolving sets with the minimum size for (CnPk)Pm(C_n\Box P_k)\Box P_m.

Keywords

Cite

@article{arxiv.2108.08733,
  title  = {Metric dimension, doubly resolving set and strong metric dimension for $(C_n\Box P_k)\Box P_m$},
  author = {Jia-Bao Liu and Ali Zafari},
  journal= {arXiv preprint arXiv:2108.08733},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2103.15560