The Subgraphs of Order Six of the Family of Strongly Regular Graphs with Parameters $\lambda=1$ and $\mu=2$

TL;DR

This paper classifies all subgraphs of order six within the family of strongly regular graphs characterized by parameters λ=1 and μ=2, contributing to understanding their structural properties.

Contribution

It provides a complete enumeration of all subgraphs of order six for this specific family of strongly regular graphs, a task not previously accomplished.

Findings

All subgraphs of order six are identified and characterized.

The structure of these subgraphs reveals insights into the symmetry of the parent graphs.

Results aid in understanding the existence and construction of such graphs.

Abstract

Strongly regular graphs are highly symmetrical and can be described fully with just a few parameters yet the existence of many of them is still under the question. Due to this uncertainty, it is of immense interest to study their structure, in particular to obtain all the possible subgraphs of lower order. In this paper we study the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$ and establish all their subgraphs of order six.