Unique Strong Isolate Semitotal Domination in Graphs

Objective: This study introduces a new domination parameter called “Unique strong isolate semitotal domination”. Methods: A unique strong isolated semitotal dominating set(USISTD-set) D of a graph G is an isolated semitotal dominating set(ISTD-set) in which there exists exactly one vertex such that . Findings: This study gives the USISTD-number of some special graphs. Also, it discusses about the non-existence of USISTD-number in some graphs. Novelty: A few findings of a new domination parameter called unique strong islolate semitotal domination of some special graphs have been established. AMS subject classification: 05C69 Keywords: Isolate semitotal domination, Unique strong isolate semitotal domination, Comb graph, Helm graph, Flower graph, Excellent graph