Given a set $ X $ of the automorphisms of a graph $ \Gamma $ , let $ \operatorname{Fix}(X) $ be theset of all vertices of $ \Gamma $ fixed by each automorphism in $ X $ .There are exactly 7 admissible intersection arrays of distance-regular graphswith diameter 3 and degree 44. It was proved early that no graphs exist for five of them.In this paper, we find the possibleautomorphisms of a hypothetical distance-regular graph with intersection array $ \{44,30,9;1,5,36\} $ .This is done by using Higman’smethod of working with automorphisms of a distance-regular graph.The main result yields the following: Let $ \Gamma $ be a distance-regular graph with intersection array $ \{44,30,9;1,5,36\} $ and let the group $ G=\operatorname{Aut}(\Gamma) $ actvertex-transitively. Then $ G $ acts intransitively on the arcs of $ \Gamma $ .
