Semitotal domination of Harary graphs

Z. Kartal, A. Aytaç

Let G be a simple finite undirected and an isolate-free graph. A set S of vertices in G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of such a set. In this paper, we study the semitotal domination number for Harary graphs, which was first introduced by Frank Harary. Since Harary graphs have the maximum possible connectivity with the minimum number of edges, many researchers are interested in studying its stability properties. In this paper, first we introduce new subclasses of analytic and bi-univalent functions defined by fractional derivative operator in the open unit disk and then for the functions belongs to these classes obtain upper bounds for the initial coefficients.

Tbilisi Mathematical Journal, Vol. 13(3) (2020), pp. 11-17