PBIB-DESIGNS AND ASSOCIATION SCHEMES FROM MINIMUM SPLIT DOMINATING SETS OF CERTAIN JUMP SIZES OF CIRCULANT GRAPHS

A dominating set D of a graph G = (V, E) is a split dominating set if the induced subgraph ⟨V-D⟩ is disconnected. The split domination number γ_s(G) is the minimum cardinality of a split dominating set of G. The set of vertices is a γ_s- set if it is split dominating set with γ_s(G). In this paper, we obtain the total number of γ_s-sets, the Partially Balanced Incomplete Block (PBIB)-Designs on γ_s-sets of certain jump sizes of Circulant graphs with m-association schemes for 1≤ m≤⌊ p/2⌋.