TY - JOUR

T1 - On the Dominant Local Metric Dimension of Corona Product Graphs

AU - Umilasari, Reni

AU - Susilowati, Liliek

AU - Slamin,

AU - Prabhu, Savari

N1 - Funding Information:
Manuscript received January 4, 2022; revised October 21, 2022. This work was supported by DRPM, KEMENRISTEK of Indonesia, Dcree 8/E1/KPT/2021, Contract No.4/E1/KP.PTNBH/2021 and 460/UN3.15/PT/2021, year 2021.
Publisher Copyright:
© 2022,IAENG International Journal of Applied Mathematics. All Rights Reserved.

PY - 2022/6

Y1 - 2022/6

N2 - A nontrivial connected graph T which one of the vertex is v, v is said to distinguish two vertex u; t if the distance between v and u is different from v to t, where u,t (Formula Presented) V (T). Metric dimension is one topic in graph theory that uses the concept of distance. Combining the definition of the local metric dimension and dominating set, there is a new term, we called it dominant local metric dimension and symbolized as Ddiml(T). An ordered subset Wl = {w1,w2,…,wn}(Formula Presented)V (T) is called a dominant local resolving set of T if Wl is a local resolving set as well as a dominating set of T. The goal of this paper’s research is to determine precise values of dominant local metric dimension for the corona product graphs. n copies of the graphs P1,P2,…,Pn of P are made to constructed the corona of any two graph T and P. After that, we link the i-th vertex of T to the vertices of Pi, where n is an order of graph T. T corona P is symbolized by T(Formula Presented)P.

AB - A nontrivial connected graph T which one of the vertex is v, v is said to distinguish two vertex u; t if the distance between v and u is different from v to t, where u,t (Formula Presented) V (T). Metric dimension is one topic in graph theory that uses the concept of distance. Combining the definition of the local metric dimension and dominating set, there is a new term, we called it dominant local metric dimension and symbolized as Ddiml(T). An ordered subset Wl = {w1,w2,…,wn}(Formula Presented)V (T) is called a dominant local resolving set of T if Wl is a local resolving set as well as a dominating set of T. The goal of this paper’s research is to determine precise values of dominant local metric dimension for the corona product graphs. n copies of the graphs P1,P2,…,Pn of P are made to constructed the corona of any two graph T and P. After that, we link the i-th vertex of T to the vertices of Pi, where n is an order of graph T. T corona P is symbolized by T(Formula Presented)P.

KW - Dominating set

KW - Local metric dimension.

KW - Local resolving set

KW - Metric dimension

UR - http://www.scopus.com/inward/record.url?scp=85143778084&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85143778084

SN - 1992-9978

VL - 52

JO - IAENG International Journal of Applied Mathematics

JF - IAENG International Journal of Applied Mathematics

IS - 4

M1 - IJAM_52_4_38

ER -