On the solution of the Graph Isomorphism Problem Part 1

TL;DR

This paper explores transforming vertex graphs into edge graphs to address the graph isomorphism problem, proposing theorems that enable effective algorithms without prior graph plotting, and discusses NP-completeness implications.

Contribution

It introduces new theorems for converting vertex graphs to edge graphs, aiding in solving graph isomorphism and enumeration problems efficiently.

Findings

Theorems for vertex-to-edge graph conversion

Effective algorithms for graph isomorphism

Insights into NP-completeness from graph transformations

Abstract

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the help of the effective algorithms without their preliminary plotting, etc. The examining of the transformation of the vertex graphs into the edge graph and the opposite operation illustrates the reasons of the appearance of the 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 the NP-completeness.