Total Domination Type Invariants of Regular Dendrimer

Abstract

Dendrimers are used in chemistry, textile engineering and related fields. Thus they are well studiedmaterials. Graphs represents; structural formula of molecules, electric circuits, networks and distributionchannels. Therefore they are used in many areas. Domination is a graph invariant which is used forinvestigation of some properties of the mentioned areas. Dendrimers are highly branched materials. Thusnumber of vertices form a geometric serie. We investigate some total domination type invariants ofregular dendrimers. In this paper total vertex-edge domination number and total edge-vertex dominationnumber are calculated for regular dendrimer graphs. New equations are obtained for regular dendrimersby using geometric series properties.