Strongly Regular Multigraphs

The chapter begins by defining strongly regular graphs and their parameters, emphasizing the significance of their adjacency eigenvalues. It then introduces the concept of multigraphs and explores how uniformly inflating the edges of a strongly regular graph results in multigraphs with distinct eigenvalues. The chapter also discusses t-designs and balanced incomplete block designs (BIBDs), highlighting their relationship with strongly regular graphs. It provides constructions for the Petersen graph from designs and explains how quasi-symmetric designs give rise to strongly regular graphs. The chapter concludes by presenting methods to generate strongly regular multigraphs from designs and outlines potential future research directions in this area.