The Forcing Geodetic Cototal Domination Number of a Graph

Abstract

Let be a geodetic cototal domination set of . A subset is called a forcing subset for if is the unique minimum geodetic cototal domination set containing . The minimum cardinality T is the forcing geodetic cototal domination number of S is denotedby , is the cardinality of a minimum forcing subset of S. The forcing geodetic cototal domination number of ,denoted by , is , where the minimum is takenover all -sets in . Some general properties satisfied by this concept arestudied. It is shown that for every pair of integers with ,there exists a connected graph such that and . where isthe geodetic cototal dominating number of .

Keywords

• geodetic set, cototal dominating set, geodetic cototal dominating set, geodetic cototal domination number,forcing geodeticcototal domination number.