TY - GEN

T1 - Nonlocal Edge Metric Dimension on Corona Multiproduct Graphs

AU - Rinurwati,

AU - Setyawati, D. W.

AU - Soleha,

AU - Herisman, I.

AU - Baihaqi, K.

AU - Sadjidon,

AU - Haryadi, T. I.

N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

PY - 2024

Y1 - 2024

N2 - The nonlocal metric dimension of a graph G, denoted dimnlG is known as the cardinality of the smallest nonlocal resolving set W in G. W resolve any vertices u and v that are not adjacent in G based on the distance from u and v to each vertex in W. In this study, a subset of vertices WE is called a nonlocal edge resolving set in G if WE resolve any two edges ei and ej in G where both are not adjacent. Thus, ei and ej have different representations to WE. The cardinality of minimum WE is called the nonlocal edge metric dimension and is denoted by edimnlG. The purpose of this study is to introduce the concept of nonlocal edge metric dimensions and further analyze graphs with certain neighboring characteristics. In this study, a multiproduct corona graph G⊙kH was used. The graph G⊙kH was obtained from (G⊙k-1H)⊙H. The research was conducted by reviewing the literature and constructing several multiproduct corona graphs for analysis of nonlocal edge metric dimension value patterns. The output of this research is getting the form of new characteristics and theorems regarding metric dimensions of nonlocal edges, especially in multiproduct corona graphs.

AB - The nonlocal metric dimension of a graph G, denoted dimnlG is known as the cardinality of the smallest nonlocal resolving set W in G. W resolve any vertices u and v that are not adjacent in G based on the distance from u and v to each vertex in W. In this study, a subset of vertices WE is called a nonlocal edge resolving set in G if WE resolve any two edges ei and ej in G where both are not adjacent. Thus, ei and ej have different representations to WE. The cardinality of minimum WE is called the nonlocal edge metric dimension and is denoted by edimnlG. The purpose of this study is to introduce the concept of nonlocal edge metric dimensions and further analyze graphs with certain neighboring characteristics. In this study, a multiproduct corona graph G⊙kH was used. The graph G⊙kH was obtained from (G⊙k-1H)⊙H. The research was conducted by reviewing the literature and constructing several multiproduct corona graphs for analysis of nonlocal edge metric dimension value patterns. The output of this research is getting the form of new characteristics and theorems regarding metric dimensions of nonlocal edges, especially in multiproduct corona graphs.

KW - Nonlocal edge metric dimension

KW - Nonlocal edges representation

KW - Nonlocal edges resolving set

UR - http://www.scopus.com/inward/record.url?scp=85200652205&partnerID=8YFLogxK

U2 - 10.1007/978-981-97-2136-8_25

DO - 10.1007/978-981-97-2136-8_25

M3 - Conference contribution

AN - SCOPUS:85200652205

SN - 9789819721351

T3 - Springer Proceedings in Mathematics and Statistics

SP - 353

EP - 360

BT - Applied and Computational Mathematics - ICoMPAC 2023

A2 - Adzkiya, Dieky

A2 - Fahim, Kistosil

PB - Springer

T2 - 8th International Conference on Mathematics: Pure, Applied and Computation, ICoMPAC 2023

Y2 - 30 September 2023 through 30 September 2023

ER -