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DCC Linear Congruential Graphs: A New Class of Interconnection Networks
February 1996 (vol. 45 no. 2)
pp. 156-164

Abstract—Let n be an integer and F = {fi : 1 ≤it 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 xV is adjacent to fi(x) mod n, 1 ≤it. For a linear function $\sl g$, and a subset V1 of V we define a linear congruential graph $G(F,\,\,n,\,\,{\sl g},\,\,V_1)$ as a graph on vertex set V, in which any xV is adjacent to fi(x) mod n, 1 ≤it , and any xV1 is also adjacent to ${\sl g}(x)$ mod n.

These graphs generalize several well known families of graphs, e.g., the de Bruijn 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.

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Index Terms:
Graph theory, interconnectons networks, network design, parallel processing, computer networks.
J. Opatrny, D. Sotteau, N. Srinivasan, K. Thulasiraman, "DCC Linear Congruential Graphs: A New Class of Interconnection Networks," IEEE Transactions on Computers, vol. 45, no. 2, pp. 156-164, Feb. 1996, doi:10.1109/12.485369
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