On Subset Labeling of Some Classical Graph Families
DOI:
https://doi.org/10.5281/zenodo.21544146Keywords:
Subset Labeling, Subset Index, Vertex Labeling, Crown Graph, Pan Graph, Wheel Graph, Gear GraphAbstract
Let be a nontrivial connected simple graph. For , let denote the family of all nonempty subsets of . A subset labeling of is a vertex labeling such that for any distinct vertices , the edge if and only if . The subset index of , denoted , is the minimum integer such that a subset labeling of exists. In this paper, we investigate the behavior of the subset index and construct valid subset labelings for several classical graph families. In particular, we determine the subset index of crown, pan, wheel, and gear graphs, and provide explicit constructions of their proper subset labelings.
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