On Graph-Transversal Designs and Graph-Authentication Codes Based on Mutually Orthogonal Graph Squares

Combinatorial designs have many interesting and genuine wide applications in areas including analysis design of algorithms, cryptography, experiments, storage system design, tournament scheduling, optical communications, computer networks to mention just a few areas. In this paper, we are concerned with the transversal authentication codes as direct combinatorial designs. The novelty current paper is demonstrated by fact that it first introduce mutually orthogonal graph squares (MOGS); call them graph-transversal graph-authentication codes, respectively. Here, major contributions constructions based on several classes graphs. Also, present results such path-transversal designs, cycle-transversal disjoint unions stars-transversal