There exists no distance-regular graph with intersection array {56,36,9;1,3,48}

TL;DR

This paper proves the non-existence of a specific distance-regular graph with a given intersection array, contributing to the classification of such graphs.

Contribution

It establishes that no distance-regular graph exists with the intersection array {56,36,9;1,3,48}, resolving a previously open question.

Findings

Proves non-existence of the specified graph.

Completes classification for certain intersection arrays.

Supports the feasibility table in existing literature.

Abstract

We prove that a distance-regular graph with intersection array {56,36,9;1,3,48} does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distance-regular graphs"\ by A.E. Brouwer, A.M. Cohen, A. Neumaier.