On Shilla graphs with b2=c2 having eigenvalue 2=0

The Shilla graph with b2=c2 and eigenvalue θ2=0 has intersection array {b(b+1)s,(bs+s+1)(b-1),bs;1,bs,(b2-1)s}. There are only seven graphs out of 55 with b3+6s2+2s,4s3+4s2+2s,2s2+s;1,2s2+s,4s3+4s2}. This paper studies the Shilla graphs with b2=c2, eigenvalue θ2=0 and intersection array {4𝑠3+6𝑠2+2𝑠,4𝑠3+4𝑠2+2𝑠,2𝑠2+𝑠;1,2𝑠2+𝑠,4𝑠3+4𝑠2}.