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 -