# Distance-regular graphs without 4-claws

## TL;DR

This paper classifies certain distance-regular graphs with diameter at least 3 that do not contain a specific type of induced subgraph, expanding understanding of their structural properties.

## Contribution

It provides a complete characterization of distance-regular graphs with diameter ≥ 3 and no induced K_{1,4} subgraphs, under the condition c_2 ≥ 2.

## Key findings

- Identifies all such graphs with the specified properties.
- Establishes structural constraints for these graphs.
- Contributes to the classification theory of distance-regular graphs.

## Abstract

We determine the distance-regular graphs with diameter at least $3$ and $c_2\geq 2$ but without induced $K_{1,4}$-subgraphs.