There exists no distance-regular graph with intersection array {55,36,11;1,4,45}

TL;DR

This paper proves the non-existence of a specific distance-regular graph with a given intersection array, confirming a conjecture from existing tables of feasible parameters.

Contribution

It provides a rigorous proof that no distance-regular graph exists with the specified intersection array from the known feasible parameter list.

Findings

Proves the non-existence of the specified distance-regular graph.

Confirms the accuracy of the feasible parameter table in prior literature.

Advances understanding of the constraints on distance-regular graphs.

Abstract

We prove that a distance-regular graph with intersection array $\{55,36,11;1,4,45\}$ 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.