TY - GEN

T1 - The Dominant Metric Dimension On The Vertex Amalgamation Product Graph

AU - Estuningsih, N.

AU - Damayanti, T. W.

AU - Susilowati, L.

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

PY - 2023/12/22

Y1 - 2023/12/22

N2 - The dominant metric dimension is the result of the development of graph theory, especially in the study of metric dimensions. The purpose of this research is to determine the dominant metric dimension on the vertex amalgamation v01 and v02, which are terminal vertices of graphs G1 and G2, respectively. The terminal vertex is a certain vertex that is set to each element of the graph collection that is carried out by the vertex amalgamation product. The vertex amalgamation product in this research is carried out on several special graphs including a complete bipartite graphs, a cycle graphs, a complete graphs, and a star graphs. From this research, it is found that Ddim(AmalG1; G2, v01; v02 ) is the sum of the dominant metric dimensions of graphs G1 and G2 minus one or minus two where G1 and G2 are a complete bipartite graphs, a cycle graphs, a complete graphs and a star graphs.

AB - The dominant metric dimension is the result of the development of graph theory, especially in the study of metric dimensions. The purpose of this research is to determine the dominant metric dimension on the vertex amalgamation v01 and v02, which are terminal vertices of graphs G1 and G2, respectively. The terminal vertex is a certain vertex that is set to each element of the graph collection that is carried out by the vertex amalgamation product. The vertex amalgamation product in this research is carried out on several special graphs including a complete bipartite graphs, a cycle graphs, a complete graphs, and a star graphs. From this research, it is found that Ddim(AmalG1; G2, v01; v02 ) is the sum of the dominant metric dimensions of graphs G1 and G2 minus one or minus two where G1 and G2 are a complete bipartite graphs, a cycle graphs, a complete graphs and a star graphs.

UR - http://www.scopus.com/inward/record.url?scp=85181562994&partnerID=8YFLogxK

U2 - 10.1063/5.0181059

DO - 10.1063/5.0181059

M3 - Conference contribution

AN - SCOPUS:85181562994

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 -