<![CDATA[Metric coloring is an extension of vertex coloring that combines the coloring concept with distance through code representations. The study of the metric chromatic number continues to develop because different graph structures may exhibit distinct coloring patterns. However, the metric chromatic number of graphs obtained through the shackle operation on tree families has not been extensively studied. This study aims to determine the metric coloring patterns and the metric chromatic numbers of the graphs and . The research employed an exploratory qualitative method with a deductive axiomatic approach. Data were obtained through mathematical observation of graph structures and documentation of relevant references. The analysis involved graph construction, determination of the order and size, formulation of labeling functions, construction of color classes, determination of code representations, and mathematical proof. The results show that and , whether the linking vertices are even-indexed or odd-indexed. These findings indicate that the partition into two color classes, together with the distance of each vertex to the classes, gives distinct code representations to every pair of adjacent vertices, because both graphs are trees and therefore bipartite. The number of leaves of the star and the length of the broom handle do not affect the result.]]>
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