PBIB-DESIGNS AND MATRIX FORM OF ASSOCIATION SCHEMES ARISING FROM MINIMUM EDGE COVERING SETS OF SOME CIRCULANT GRAPHS

Let G = (V, E) be a graph. The smallest number of edges in any edge cover of G and is called its edge covering number α1 In this paper, we obtain the total number of α1-sets, the Partially Balanced Incomplete Block (PBIB)- Designs on minimum α1-sets of Circulant graphs with m-association schemes for 1 ≤ m ≤ ⌊ p 2 ⌋.