Two characterizations of the grid graphs

TL;DR

This paper provides two new characterizations of grid graphs as co-edge-regular graphs with four distinct eigenvalues, enhancing understanding of their algebraic and combinatorial properties.

Contribution

It introduces two novel characterizations of grid graphs based on spectral and regularity properties, expanding the theoretical framework for analyzing such graphs.

Findings

Grid graphs are characterized as co-edge-regular with four eigenvalues.

The characterizations offer new insights into the algebraic structure of grid graphs.

These results may facilitate further research in algebraic graph theory.

Abstract

In this paper we give two characterizations of the $p \times q$-grid graphs as co-edge-regular graphs with four distinct eigenvalues.