ENUMERATION INTERSECTION ARRAYS OF SHILLA GRAPHS WITH B = 6

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 \(b=6\).