Friday, October 28, 2011
Hall 1-2 (San Jose Convention Center)
Directed strongly regular graphs were rst studied by A. Duval in 1988 as generalizedobjects of strongly regular graphs. Directed strongly regular graphs are obtained fromvarious combinatorial objects, including Cayley graphs, block designs, Hadamard matrices, nite geometries (projective and ane geometries), and partial geometries. There arenumber of in nite families of directed strongly regular graphs that are constructed on the
ags or anti-ags of certain nite incidence structures. These directed strongly regulargraphs satisfy certain parameter conditions. We show that the necessary conditions for a nite incidence structure to give rise to a directed strongly regular graph with certainparameter sets are indeed sucient. We also show that the directed strongly regulargraphs that obtained from the ags of certain di erence sets and Hadamard designs, havevertex-trantive automorphism groups.A
ags or anti-ags of certain nite incidence structures. These directed strongly regulargraphs satisfy certain parameter conditions. We show that the necessary conditions for a nite incidence structure to give rise to a directed strongly regular graph with certainparameter sets are indeed sucient. We also show that the directed strongly regulargraphs that obtained from the ags of certain di erence sets and Hadamard designs, havevertex-trantive automorphism groups.A