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Resolvability in Hypergraphs

Imran Javaid, Azeem Haider, Muhammad Salman, Sadaf Mehtab

Abstract

This article emphasizes an extension of the study of metric and par- tition dimension to hypergraphs. We give a sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified conditions.eral and give exact values with specified conditions.

Resolvability in Hypergraphs

Abstract

This article emphasizes an extension of the study of metric and par- tition dimension to hypergraphs. We give a sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified conditions.eral and give exact values with specified conditions.

Paper Structure

This paper contains 3 sections, 21 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Metric Dimension of Hypergraphs
  3. Partition Dimension of Hypergraphs

Key Result

Proposition 2.1

For any two distinct vertices $u, v\in C(i_1,i_2,...,i_d)$, we have $d(u,w)=d(v,w)$ for any $w\in V(H)\setminus\{u,v\}.$

Theorems & Definitions (34)

  • Proposition 2.1
  • Lemma 2.2
  • Proposition 2.3
  • proof
  • Remark 2.4
  • Theorem 2.5
  • proof
  • Corollary 2.6
  • Example 2.7
  • Example 2.8
  • ...and 24 more