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 -