TY - GEN

T1 - Local Multiset Dimension of Amalgamation Cycle

AU - Alfarisi, Ridho

AU - Susilowati, Liliek

AU - Dafik,

N1 - Publisher Copyright:
© 2023 American Institute of Physics Inc.. All rights reserved.

PY - 2023/12/22

Y1 - 2023/12/22

N2 - One of the topics of distance in graphs is resolving set problems. Suppose the set W = {s1, s2,. . ., sk} ⊂ V(G), the vertex representations of ∈ V(G) is rm(x|W) = {d(x, s1), d(x, s2),. . ., d(x, sk)}, where d(x, si) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if rm(v|W) ≠ rm(u|W) for uv ∈ E(G). The local m-resolving set having minimum cardinality is called the local multiset basis and it’s cardinality is called the local multiset dimension of G, denoted by mdl(G). In our paper, we determined the local multiset dimension of amalgamation of cycles.

AB - One of the topics of distance in graphs is resolving set problems. Suppose the set W = {s1, s2,. . ., sk} ⊂ V(G), the vertex representations of ∈ V(G) is rm(x|W) = {d(x, s1), d(x, s2),. . ., d(x, sk)}, where d(x, si) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if rm(v|W) ≠ rm(u|W) for uv ∈ E(G). The local m-resolving set having minimum cardinality is called the local multiset basis and it’s cardinality is called the local multiset dimension of G, denoted by mdl(G). In our paper, we determined the local multiset dimension of amalgamation of cycles.

UR - http://www.scopus.com/inward/record.url?scp=85181570885&partnerID=8YFLogxK

U2 - 10.1063/5.0181077

DO - 10.1063/5.0181077

M3 - Conference contribution

AN - SCOPUS:85181570885

T3 - AIP Conference Proceedings

BT - AIP Conference Proceedings

A2 - Pusporani, Elly

A2 - Millah, Nashrul

A2 - Hariyanti, Eva

PB - American Institute of Physics Inc.

T2 - International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022

Y2 - 2 October 2022 through 3 October 2022

ER -