In Graph Theory, independent number and, dominating number are three of the important parameters to measure the resilience of graphs, respectively denoted by and for a graph . But predecessors have proved that computing them are very hard. So computing and of some particular known graphs is extremely valuable. In this paper, we determine and of -star graphs, denoted by , followed by some relative conclusions of -star, denoted by as the isomorphism of . In addition, our method giving dominating set of is more easily understood than [7], which presented a broadcast algorithm to determine dominating set of. DOI: http://dx.doi.org/10.11591/telkomnika.v11i1.1901