On the diameter and zero forcing number of some graph classes in the Johnson, Grassmann and Hamming association scheme

TL;DR

This paper investigates the diameter and zero forcing number of specific graph classes within Johnson, Grassmann, and Hamming schemes, extending known results in algebraic graph theory.

Contribution

It provides new determinations of diameter and zero forcing numbers for generalized Grassmann, Johnson, and Hamming graphs, expanding the understanding of their structural properties.

Findings

Diameter of generalized Grassmann graphs determined

Zero forcing number of generalized Johnson graphs calculated

Zero forcing number of Hamming graphs analyzed

Abstract

We determine the diameter of generalized Grassmann graphs and the zero forcing number of some generalized Johnson graphs, generalized Grassmann graphs and the Hamming graphs. Our work extends several previously known results.