DCC linear congruential graphs: A new class of interconnection networks

Let n be an integer and F = {f(i): 1 less than or equal to i less than or equal to t for some integer t} be a finite set of linear functions. We define a linear congruential graph G(F, n) as a graph on the vertex set V = {0, 1,..., n - 1}, in which any x is an element of V is adjacent to f(i)(x) mod n, 1 less than or equal to i less than or equal to t. For a linear function g, and a subset V-1 of V we define a linear congruential graph G(F, n, g, V-1) as a graph on vertex set V, in which any x is an element of V is adjacent to f(i)(x) mod n, 1 less than or equal to i less than or equal to t, and any x is an element of V-1 is also adjacent to g(x) mod n. These graphs generalize several well known families of graphs, e.g., the de 8ruijn graphs. We give a family of linear functions, called DCC linear functions, that generate regular, highly connected graphs which are of substantially larger order than de Bruijn graphs of the same degree and diameter. Some theoretical and empirical properties of these graphs are given and their structural properties are studied.