TY - GEN
T1 - Study on mixed metric dimension of STAR and its Comb product with path
AU - Darmaji,
AU - Azahra, Nadia
AU - Alfarisi, Ridho
N1 - Publisher Copyright:
© 2022 Author(s).
PY - 2022/12/19
Y1 - 2022/12/19
N2 - 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 Rm ⊂V (G). The set Rm 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 dimm(G), i.e. the smallest amount of elements of a mixed resolving set Rm in G. In this research, we consider the mixed metric dimension of star graph Sn 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 Sn and it's comb operation, those are Pm ▹ Sn and Sm ▹ Pn.
AB - 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 Rm ⊂V (G). The set Rm 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 dimm(G), i.e. the smallest amount of elements of a mixed resolving set Rm in G. In this research, we consider the mixed metric dimension of star graph Sn 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 Sn and it's comb operation, those are Pm ▹ Sn and Sm ▹ Pn.
UR - http://www.scopus.com/inward/record.url?scp=85145456133&partnerID=8YFLogxK
U2 - 10.1063/5.0131874
DO - 10.1063/5.0131874
M3 - Conference contribution
AN - SCOPUS:85145456133
T3 - AIP Conference Proceedings
BT - 7th International Conference on Mathematics - Pure, Applied and Computation
A2 - Mufid, Muhammad Syifa�ul
A2 - Adzkiya, Dieky
PB - American Institute of Physics Inc.
T2 - 7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021
Y2 - 2 October 2021
ER -