Abstract
Most recent research in graph theory considered the studying of edge regular graph class ER(n,d,λ) for some n>d>λ, such that all the n vertices have d adjacent neighbors, and each pair of adjacent vertices have λ common neighbors, none of these research gave an algorithm to generate this class with considering the λ, in this paper, a novel algorithm to generate random edge-regular graphs for λ > 0. The algorithm produces an edge-regular graph for different values of d and n Moreover, it is easy to implement and quite fast in practice. The Matlab programming language used to obtain the experimental result. The analysis of this method showed that the running time of this method proven to be O(d3).
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