Hamiltonian Subgraphs of Order Seven in $srg(n,k,1,2)$

TL;DR

This paper investigates the presence of Hamiltonian subgraphs of size seven in strongly regular graphs with parameters (n,k,1,2), establishing bounds on the number of 7-cycles and advancing understanding of their structure.

Contribution

It characterizes all possible Hamiltonian subgraphs of order seven in srg(n,k,1,2) graphs and provides bounds on 7-cycle counts, extending previous structural knowledge.

Findings

Identified all Hamiltonian subgraphs of order seven in srg(n,k,1,2) graphs.

Established bounds for the number of 7-cycles in these graphs.

Contributed to the classification and structural understanding of these strongly regular 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. In this paper, we continue the study of the famuly of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$ and establish all of their possible Hamiltonian subgraphs of order seven. By doing so we establish the lower and upper bounds for number of 7-gons, or 7-cycles, in such graphs.