The strong and doubly metric dimensions of Johnson and Kneser graphs

TL;DR

This paper determines the exact strong and doubly metric dimensions of Johnson and Kneser graphs, providing new formulas and results for these graph parameters.

Contribution

It presents the exact strong metric dimensions for Johnson graphs and Kneser graphs, and computes the doubly metric dimensions for specific cases.

Findings

Exact strong metric dimension of Johnson graphs obtained.

Strong metric dimension of Kneser graphs found for n ≥ 3k-1.

Doubly metric dimensions of J_{n,2} and K_{n,2} are both rac{2n}{3}loor.

Abstract

In this paper, the strong and doubly metric dimensions of Johnson and Kneser graphs are considered. The exact value of the strong metric dimension of Johnson graph $J_{n,k}$ is obtained using the well-known results from the literature. The strong metric dimension of Kneser graph $K_{n,k}$ has been obtained for $n \ge 3k-1$. Finally, it has been shown that the doubly metric dimensions of Johnson graph $J_{n,2}$ and Kneser graph $K_{n,2}$ are both $\lceil \frac{2n}{3} \rceil$.