On Minimum Order of Odd Regular Graphs Without Perfect Matching

TL;DR

This paper determines the smallest size of odd regular graphs lacking perfect matchings, highlighting differences from even regular graphs and verifying results with Petersen's theorem.

Contribution

It derives the minimum order of odd regular graphs without perfect matchings and compares these findings to even regular graphs, confirming consistency with Petersen's theorem.

Findings

Minimum order of odd regular graphs without perfect matching

Differences between odd and even regular graphs regarding matchings

Validation of results with Petersen's theorem

Abstract

In this article we have derived the minimum order of an odd regular graph such that the graph has no matching. We have observed that how it is different from the case of even regular graphs. We have checked the consistency of the derived result with Petersen's theorem.