Isolate Domination Decomposition of Tensor Product of Cycle Related Graphs

Objectives: This study deals about tensor product of some cycle related graphs which admits an IDD. Methods: We have a decomposed a graph into parts in such a way that the isolate domination number of partitions ranges from to . We have used basic terms and propositions of isolate domination over the graph in order to obtain the results. Findings: We have introduced Isolate Domination Decomposition (IDD) of Graphs 1 and is defined as a collection of subgraphs of such that every edge of belongs to exactly one each is connected and it contains atleast one edge and . Also we have found the range of vertices for a graph under which the conditions of IDD are satisfied along with the converse part. Novelty: Domination and Decomposition are widely used in networking, block design, coding theory and many fields. Motivated by the concept of ascending pendant domination and decomposition 2, 3, we have used here the isolate domination combined with decomposition to characterize the graphs which admits this new parameter and to investigate their vertex bounds. Keywords: Dominating Set, Domination Number, Isolate Dominating Set, Decomposition, Isolate Domination Decomposition, Tensor Product, Cycle Related Graph