Dimensi Metrik pada Graf Hasil Operasi Join pada Graf Lengkap dan Graf Tangga

Deddy Rahmadi (Universitas Islam Negeri Sunan Kalijaga Yogyakarta)
Awal Febriantono (Universitas Islam Negeri Sunan Kalijaga Yogyakarta)
Nurul Mufidah (Universitas Islam Negeri Sunan Kalijaga Yogyakarta)
Tsalis Wifqi Hidayati (Universitas Islam Negeri Sunan Kalijaga Yogyakarta)
Maulidatu Jauharoti Alisyah (Universitas Islam Negeri Sunan Kalijaga Yogyakarta)

Square : Journal of Mathematics and Mathematics Education
Vol. 7 No. 1 (2025)

The metric dimension of a graph is defined as the minimum cardinality of a resolving set of the graph. This study aims to determine the metric dimension of graphs obtained from the join operation between a complete graph and a ladder graph. The analysis begins by determining the metric dimensions of the constituent graphs, namely the complete graph K_n and the ladder graph L_m. Furthermore, the metric dimension of the graph resulting from the join operation K_n + L_m is investigated. The results show that the metric dimension of the complete graph K_n is n-1, the metric dimension of the ladder graph L_m is 2, and the metric dimension of the graph K_n+L_m is n+1.