A Converting of the Directed Graphs

TL;DR

This paper explores the conversion processes between directed graphs and their implications for understanding NP-completeness, building on previous work to analyze graph transformations and their computational complexity.

Contribution

It introduces a detailed examination of vertex-to-edge graph transformations and discusses their role in the emergence of NP-completeness in graph theory.

Findings

Transformation of graphs explains NP-completeness origins

Vertex and edge graph conversions analyzed

Implications for solving NP-complete problems

Abstract

The presented material continues the previous article (arxiv:1007.1059) and also is devoted to the equivalent conversion between the graphs. The examining of the transformation of the vertex graphs into the edge graphs (together with the opposite transformation) illustrates the reasons of the appearance of NP-completeness from the point of view of the graph theory. We suggest that it also illustrates the synchronous possibility and impossibility of the struggle with NP-completeness.