On H-Irregularity Strength of Grid Graphs

TL;DR

This paper determines the exact H-irregularity strength values for grid graphs, which are the minimum labeling values needed for vertex, edge, and total irregularity, advancing understanding of graph covering properties.

Contribution

It provides the exact values of H-irregularity strength for grid graphs with grid-covering, a novel contribution to graph labeling theory.

Findings

Exact H-irregularity strength values for grid graphs are established.

Results apply specifically to graphs admitting grid-covering.

Advances understanding of graph labeling in grid structures.

Abstract

This paper deals with three graph characteristics related to graph covering named the (vertex, edge, and total, resp.) H-irregularity strength of a graph G admitting H-covering. Those are the minimum values of positive integer k such that G has an H-irregular (vertex, edge, and total, resp.) k-labeling. The exact values of these three characteristics are determined for grid graph admitting grid-covering