A solution to an open problem on lower against number in graphs

TL;DR

This paper addresses an open problem by establishing a tight lower bound on the lower against number of any graph based on its order and maximum degree, advancing understanding in graph theory.

Contribution

It provides the first definitive solution to the open problem by deriving a precise lower bound for the lower against number in general graphs.

Findings

Established a tight lower bound on lower against number

Expressed the bound in terms of graph order and maximum degree

Solved a previously open problem in graph theory

Abstract

In [1] the problem of finding a sharp lower bound on lower against number of a general graph is mentioned as an open question. We solve the problem by establishing a tight lower bound on lower against number of a general graph in terms of order and maximum degree.