Degree/Diameter , , Cayley G

iv The Degree/Diameter problem has been studied for a long time and still have’t been solved completely.We take a whole analysis on it and give two main solutions to it in this paper.One is through constructing a Cayley graph on the semi-product of two cyclic groups,another is by lifting a small base graph G in a cyclic group Znp through a voltage assignment α.We focus on the fundamental theory and computing steps of the two methods,and give an example for each. By building the relation among diameter,eigenvalue and degree of a regular graph,we got a so-called Eigenvalue-Δ Bound compared famous Moore Bound. Sur-prisingly,the Eigenvalue-Δ Bound is equal to the Moore Bound for all the cases with diameter 2.Along the method,we discussed all the possible degree value of Moore Graph with Diameter 2,and consequently,got all the possible Moore Graphs. Finally,we proposed a few value-questions and guesses,also suggestions for this problem as a first try to consider this problem form a new perspective