About the finding of independent vertices of a graph

TL;DR

This paper explores the Maximum Independent Set Problem in graphs, demonstrating its relation to twin-orthogonal graphs and establishing properties for trivial cases, contributing to graph theory and combinatorial optimization.

Contribution

It introduces a novel approach linking the problem to twin-orthogonal graphs and formulates a dual problem, providing insights into maximal independent sets in special graph classes.

Findings

Maximum independent set problem relates to twin-orthogonal graphs.

In trivial twin-orthogonal graphs, maximal independent sets are also maximum.

Dual problem formulation offers new perspectives in graph optimization.

Abstract

We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is formulated which is dual to the problem above. It is shown that, for trivial twin-orthogonal graphs, any of its maximal independent set is also maximum one.