Graphs Associated with (0,1) Arrays.

Several classes of graphs defined on arbitrary n-dimensional (0,1) arrays are introduced. These classes of graphs have as their point set the set of 1's of the array. Different classes are distinguished by the manner in which adjacency is defined. Characterizations are obtained for all these classes of graphs. Let G be a graph. The classes of graphs defined on the adjacency, incidence, and clique-vertex matrices are related to properties of G. A new method of representing graphs is introduced. The points of the graph are represented by ordered n-tuples of integrers and two n-tuples are adjacent whenever they agree on one or more coordinates. Some of the applications of these classes of graphs include the consecutive 1's property of (0,1) matrices, switching theory minimization, circulant matrices, latin squares, a representation theory for directed graphs, and a graphical decomposition of automata. (Author)
Report on the Theory and Applications of Automation Theory.