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Bankapur, Veena; Basha, Shaikh Ameer; Chaluvaraju, B
International journal of mathematical combinatorics, 09/2023, Volume: 3Journal Article
The pairwise balanced designs (PB_D's) is a pair (P, B), where P is a finite set of v points and В is a family of subsets of P, called blocks such that every two distinct points in P appear in exactly one block. Let a(G) = a and /3(G) = ß be the vertex covering and independence number of a graph G = (V, B) with the minimum and maximum cardinality of such sets are denoted by а-sets and /3-sets of G, respectively (or, simply (a,/3)-sets). In this paper, we obtain the total number of (a, /3)-sets in different jump sizes of some circulant graphs apart from strongly regular graphs which are the blocks of PBD.
