ITSITS

(IJCSAM) International Journal of Computing Science and Applied Mathematics(IJCSAM) International Journal of Computing Science and Applied Mathematics

Given a connected G = (V (G), E(G)) graph. The main problem in graph metric dimensions is calculating the metric dimensions and their characterization. In this research, a new dimension concept is introduced, namely a bi-edge metric dimension of graph which is a development of the concept of bi-metric graphs with the innovation of bi-metric graph representations to become the bi-edge metric graph representations. In this case, what is meant by bi-edge metric and edge detour. If there is a set in G that causes every edge in G has a different bi-edge metric representation in G, then that set is called the bi-edge metric resolving set. The minimum cardinality of the bi-edge metric resolving set graphs is called the bi-edge metric dimension of G graph, denoted by e dimb(G). The specific purpose of this research is to apply the concept of bi-edge metric dimensions to special graphs, such as cycle, complete, star and path can be obtained.

From this research, the exact values of a bi-edge metric dimension are obtained for several special graphs, namely cycle, complete, star and path.Based on the results that have been obtained, this research can be developed to determine the bi-edge metric dimension on graphs resulting such as graphs resulting from corona operations.The authors express gratitude to the Department of Mathematics ITS for their support and to the referees for their helpful suggestions and comments.

Penelitian lebih lanjut dapat dilakukan dengan mengeksplorasi penerapan konsep dimensi bi-edge metrik pada graf yang dihasilkan dari operasi graf, seperti graf corona. Selain itu, studi tentang varian konsep dimensi bi-metrik dan dimensi bi-metrik dari operasi graf yang dihasilkan juga menjanjikan. Pengembangan metode baru, seperti kombinasi metode subgraph dan pengenalan pola, dapat diterapkan pada jenis graf lain untuk menentukan dimensi bi-edge metriknya. Penelitian ini dapat diperluas dengan menyelidiki hubungan antara dimensi bi-edge metrik dengan properti graf lainnya, seperti konektivitas atau derajat simpul. Studi komparatif antara dimensi bi-edge metrik dan konsep dimensi graf lainnya, seperti dimensi metrik atau dimensi detour, dapat memberikan wawasan yang lebih dalam tentang struktur graf. Terakhir, eksplorasi aplikasi praktis dari dimensi bi-edge metrik dalam bidang seperti jaringan komputer atau analisis data juga dapat menjadi arah penelitian yang menarik.

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