There is a continuing search for dense $( \delta ,D )$ interconnection graphs, that is, regular, undirected, degree $\delta $ graphs with diameter D and having a large number of nodes. Cayley graphs formed by Borel subgroups currently contribute to some of the densest known $( \delta = 4,D )$ graphs for a range of D [1]. However, the group theoretic representation of these graphs makes the development of efficient routing algorithms difficult. In an earlier report, it was shown that all Cayley graphs have generalized chordal ring (GCR) representations [2]. In this paper, it is shown that all degree-4 Borel Cayley graphs can also be represented by the more restrictive chordal rings (CR) through a constructive proof. A step-by-step algorithm to transform any degree-4 Borel Cayley graph into a CR graph is provided. Examples are used to illustrate this concept.
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