On the Metric Dimension for Snowflake Graph

Muhammad Rafif Fajri (Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science (FMIPA), Universitas Andalas, Padang, Indonesia)
Luthfi Hadiyan Fajri (Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science (FMIPA), Universitas Andalas, Padang, Indonesia)
Jamaluddin Ashari (Department of Mathematics, Faculty of Mathematics and Natural Science (FMIPA), Universitas Negeri Padang, Padang, Indonesia)
Abdurrahman Abdurrahman (Department of Electrical Engineering, Faculty of Electrical Engineering and Computer Science, Chien Hsin University of Science and Technology（健行科技大學), Taoyuan, Taiwan.)
Alifaziz Arsyad (Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science (FMIPA), Universitas Andalas, Padang, Indonesia)

Eksakta : Berkala Ilmiah Bidang MIPA
Vol. 23 No. 04 (2022): Eksakta: Berkala Ilmiah Bidang MIPA (E-ISSN : 2549-7464)

The concept of metric dimension is derived from the resolving set of a graph, that is measure the diameter among vertices in a graph. For its usefulness in diverse fields, it is interesting to find the metric dimension of various classes of graphs. In this paper, we introduce two new graphs, namely snowflake graph and generalized snowflake graph. After we construct these graphs, aided with a lemma about the lower bound of the metric dimension on a graph that has leaves, and manually recognized the pattern, we found that dim(Snow) = 24 and dim(Snow(n,a,b,c)) = n(a+c+1).