In this paper, we generalize the construction of strongly regular graphs in Tan et al. (J. Comb. Theory, Ser. A 117:668–682, 2010) from ternary bent functions to p-ary bent functions, where p is an odd prime. We obtain strongly regular graphs with three types of parameters. Using certain non-quadratic p-ary bent functions, our constructions can give rise to new strongly regular graphs for small...

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We probabilistically compute the spectrum of the line intersection graphs of two non-isomorphic generalized quadrangles of orde...

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

In this paper the Wallis-Fon-Der-Flaass construction of strongly regular graphs is generalized. As a result new prolific series of strongly regular graphs are obtained. Some of them have new parameters.

We give a construction of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.

We give two constructions of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new parameters.

We present quantum graphs with remarkably regular spectral characteristics. We call them regular quantum graphs. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansio...

valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...