The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters $\lambda=1$ and $\mu=2$

TL;DR

This paper investigates the structural properties of strongly regular graphs with specific parameters, establishing a lower bound on the number of hexagons and linking this to the graph's existence.

Contribution

It provides the first known lower bound on the number of hexagons in strongly regular graphs with parameters λ=1 and μ=2, connecting graph existence to hexagon count.

Findings

Established a lower bound for the number of hexagons

Linked the existence of certain strongly regular graphs to their hexagon count

Provided structural insights into strongly regular graphs with given parameters

Abstract

The existence of $srg(99,14,1,2)$ has been a question of interest for several decades to the moment. In this paper we consider the structural properties in general for the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$. In particular, we establish the lower bound for the number of hexagons and, by doing that, we show the connection between the existence of the aforementioned graph and the number of its hexagons.