CHARACTERISATION OF REGULAR GRAPHS AS LOOP GRAPHS

Abstract

There have been various generalisations of Cayley graphs, prototypes of transitive graphs. The most generalised is the description of graphs on general groupoids. What has clearly emerged in this exercise is that the philosophy of constructing graphs on groupoids offers a fruitful avenue from which we may understand some aspects of graph theory. In this paper we show that a graph is regular if and only if it is a loop graph. Further, it is shown that the majority of loops which would describe a particular graph are monotopic.

Mathematics Subject Classification (2000): 08A99, 05C75, 05C25.