Determining Number of Kneser Graphs: Exact Values and Improved Bounds

TL;DR

This paper investigates the determining number of Kneser graphs, offering improved bounds and exact values for specific subfamilies, advancing understanding of graph symmetries and automorphisms.

Contribution

It provides new upper and lower bounds and calculates exact determining numbers for certain Kneser graph subfamilies, enhancing previous results.

Findings

Improved bounds on the determining number of Kneser graphs

Exact determining numbers for specific Kneser graph subfamilies

Enhanced understanding of automorphism group actions on Kneser graphs

Abstract

The determining number of a graph $G = (V,E)$ is the minimum cardinality of a set $S\subseteq V$ such that pointwise stabilizer of $S$ under the action of $Aut(G)$ is trivial. In this paper, we provide some improved upper and lower bounds on the determining number of Kneser graphs. Moreover, we provide the exact value of the determining number for some subfamilies of Kneser graphs.