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 - 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 -