Exhaustive Verification of Weak Reconstruction For Self Complementary Graphs

TL;DR

This paper develops an exhaustive method to verify weak reconstruction of Self Complementary Graphs up to 17 vertices, employing pruning techniques to optimize graph-isomorphism checks and analyzing the limitations of this approach.

Contribution

It introduces a comprehensive verification approach for Self Complementary Graphs, improving efficiency with pruning techniques and providing new enumeration data.

Findings

Verification of SC graphs up to 17 vertices achieved

Pruning techniques significantly reduce computation time

Enumeration of SC graphs up to 101 vertices provided

Abstract

This paper presents an exhaustive approach for verification of the weak reconstruction of Self Complementary Graphs up to 17 vertices. It describes the general problem of the Reconstruction Conjecture, explaining the complexity involved in checking deck-isomorphism between two graphs. In order to improve the computation time, various pruning techniques have been employed to reduce the number of graph-isomorphism comparisons. These techniques offer great help in proceeding with a reconstructive approach. An analysis of the numbers involved is provided, along with the various limitations of this approach. A list enumerating the number of SC graphs up till 101 vertices is also appended.