Towards a classification of $1$-homogeneous distance-regular graphs with positive intersection number $a_1$

Jack H. Koolen, Mamoon Abdullah, Brhane Gebremichel +1

Let $\hat{I}“$ be a graph with diameter at least two. Then $\hat{I}“$ is said to be $1$-homogeneous (in the sense of Nomura) whenever for every pair of adjacent vertices $x$ and $y$ in $\hat{I}“$, t…