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