A necessary and sufficient condition for a graph $G$, which satisfies the equality $\mu_{21}(G)=|V(G)|$

TL;DR

This paper establishes a precise condition characterizing when a graph's parameter _{21}(G) equals the number of vertices, providing a complete criterion for this equality.

Contribution

It introduces a necessary and sufficient condition for graphs to satisfy _{21}(G)=|V(G)|, advancing understanding of this graph invariant.

Findings

Derived a complete characterization for graphs with _{21}(G)=|V(G)|

Provided a new criterion for analyzing graph invariants

Enhanced theoretical understanding of graph parameters

Abstract

A necessary and sufficient condition is found for a graph $G$, which satisfies the equality $\mu_{21}(G)=|V(G)|$.