Partial geometric designs having circulant concurrence matrices

We classify small partial geometric designs (PGDs) by spectral characteristics of their concurrence matrices. It is well known that the matrix a PGD can have at most three distinct eigenvalues, all which are nonnegative integers. The contains useful information on incidence structure design. An ordinary 2- ( v , k λ ) $(v,k,\lambda )$ design has single $\lambda $ and its circulant, geometry two concurrences 1 0, transversal TD u ${\text{TD}}_{\lambda }(k,u)$ circulant. In this paper, we survey PGDs highlighting constructions. Then investigate symmetric circulant matrices realized as PGDs. particular, try to give list order up 12 each matrix. then describe these along with combinatorial properties This work part second author's Ph.D. dissertation [46].