Study on mixed metric dimension of STAR and its Comb product with path.

Consider an ordered couple V and E, which V symbolized set of vertex in graph G and E symbolized set of edge in graph G, respectively, i.e G = (V, E). Furthermore, for simplicity we call G. Assume graph G has the properties: connected, undirected, finite. We have a set of vertices, symbolized by Rm and R_m ⊂ V (G). The set R_m is known as a mixed resolving set, if every vertex or every edge in G are able to be determined by one or more vertices of Rm. The mixed metric dimension, symbolized by dim_m(G), i.e. the smallest amount of elements of a mixed resolving set R_m in G. In this research, we consider the mixed metric dimension of star graph S_n and it's comb operation. Assume K and L are any two graphs. The comb operation between them, symbolized by K ⊳ L, is a new one that formed by grafting the j-th imitate of L to the j-th vertex in K. Moreover, we precisely get value of mixed metric dimension of star graph S_n and it's comb operation, those are P_m ⊳ S_n and S_m⊳ P_n. [ABSTRACT FROM AUTHOR]