Generalized Hadamard Matrices and Generalized Hadamard Graphs

Hadamard matrices and their applications have steadily and rapidly grown during the last 2 decades. Due to that many researchers have developed various concepts on Hadamard matrices. This paper concentrates on Generalized Hadamarad matrices. In the first part of this work, some new results on construction of generalized Hadamard matrices GH(p; pn) over Cp are introduced. In the second part, graphs obtained from generalized Hadamard matrices are introduced, namely generalized Hadamard graphs. In particular, we show that the generalized Hadamard graphs are pn- regular. Our results have been illustrated by constructing pn- regular graphs for different values of p and n.