Fast recognition of some parametric graph families

TL;DR

This paper develops fast recognition algorithms for specific parametric graph families, including cycle regular I-graphs and folded cubes, by leveraging structural properties and achieving sub-logarithmic complexity.

Contribution

It introduces linear and sub-logarithmic recognition algorithms for certain cycle regular graphs, expanding the understanding of their structural properties.

Findings

Recognition algorithms for $[1, \lambda, 8]$-cycle regular I-graphs

Recognition algorithms for $[1, \lambda, 8]$-cycle regular double generalized Petersen graphs

A $o(N \log N)$ recognition algorithm for folded cubes

Abstract

We identify all $[1, \lambda, 8]$-cycle regular $I$-graphs and all $[1, \lambda, 8]$-cycle regular double generalized Petersen graphs. As a consequence we describe linear recognition algorithms for these graph families. Using structural properties of folded cubes we devise a $o(N \log N)$ recognition algorithm for them. We also study their $[1,\lambda,4]$, $[1,\lambda,6]$ and $[2, \lambda, 6]$-cycle regularity and settle the value of parameter $\lambda$.