The Lower Bound for Number of Hexagons in Strongly Regular Graphs with Parameters λ = 1 and μ = 2

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 λ=1 and μ=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.