The concept of semi-regular sets of matrices was introduced by J. Seberry in "A new construction for Williamson-type matrices", Graphs and Combinatorics, 2(1986), 81-87. A regular s-set of matrices of order m was first discovered by J. Seberry and A. L. Whiteman in "New Hadamard matrices and conference matrices obtained via Mathon's construction", Graphs and Combinatorics, 4(1988), 355-377. In ...

Let D be a non-trivial simple t-design. For 1 ≤ s ≤ t, we generalize the concept of the incidence graph of D and construct a new bipartite regular graph Γ. We obtain that the edge-transitivity of the graph Γ is equivalent to the s-flag-transitivity of the design D. We then, for s = 2, classify the semisymmetric graphs among the graphs Γ constructed from biplanes and triplanes. Finally, we study...

A graph is 1-arc-regular if its full automorphism group acts regularly on the set of its arcs. In this paper, we investigate 1-arc-regular graphs of prime valency, especially of valency 3. First, we prove that if G is a soluble group then a (G, 1)-arc-regular graph must be a Cayley graph of a subgroup of G . Next we consider trivalent Cayley graphs of a finite nonabelian simple group and obtain...