When Are Standard Graph Products Isomorphic?
Combinatorics
2025-08-07 v1
Abstract
This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected graphs for which their corresponding products are isomorphic. As a by-product, we identify a novel family of non-distance-regular graphs that possess fewer than d+1 distinct distance eigenvalues, where d represents the diameter of the graph. This result offers a new perspective on Problem 4.3 posed in [2], moving beyond the current approaches.
Keywords
Cite
@article{arxiv.2508.04137,
title = {When Are Standard Graph Products Isomorphic?},
author = {Priti Prasanna Mondal and M. Rajesh Kannan and Fouzul Atik},
journal= {arXiv preprint arXiv:2508.04137},
year = {2025}
}