Abstract
In this paper, we have shown that the arbitrary supersubdivision of a path, a cycle, a fan graph, a wheel graph, a helm graph and a gear graph by a complete bi-partite graph , for any admits star-in-coloring. In addition, we have proved the fan graph and the splitting graph of a path, a cycle and a fan graph also admit star-in-coloring. 2000 Mathematics Subject Classification: 05C15, 05C20.
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