ENUMERATION INTERSECTION ARRAYS OF SHILLA GRAPHS WITH B = 6

Abstract

Let $\Gamma$ be a distance-regular graph of diameter $3$, and let $\theta_1$ be its second eigenvalue. The graph $\Gamma$ is called a Shilla graph if $\theta_1=a_3$. In this case, $\theta_1={(a_1+\sqrt{a_1^2+4k})}/{2}$, and $a=a_3$ divides $k$ We set $b=b(\Gamma)=k/a$. J.H. Koolen and J. Park found the intersection arrays of Shilla graphs with $b\le 3$. J. Cai, I.N. Belousov, and A.A. Makhnev enumerated the intersection arrays of Shilla graphs with $b=4$. H. Li, I.N. Belousov, and A.A. Makhnev found the intersection arrays of Shilla graphs with $b=5$. In this paper, we enumerate the intersection arrays of Shilla graphs with $b=6$