$H$-supermagic labelings for firecrackers, banana trees and flowers
Rachel Wulan Nirmalasari Wijaya, Andrea, Semani\v{c}ov\'a-Fe\v{n}ov\v{c}\'ikov\'a, Joe Ryan, Thomas Kalinowski

TL;DR
This paper investigates special labelings called $H$-supermagic labelings in graphs, proving their existence for certain classes like firecrackers, banana trees, and flowers, under specific conditions.
Contribution
It establishes the existence of $H$-supermagic labelings for various graph classes, extending the theory of graph labelings with new constructions and results.
Findings
Firecracker graphs $F_{k,n}$ are $F_{2,n}$-supermagic for odd $n$
Banana trees $B_{k,n}$ are $B_{1,n}$-supermagic
Flowers $F_n$ are $C_3$-supermagic
Abstract
A simple graph admits an -covering if every edge in is contained in a subgraph of which is isomorphic to . In this case we say that is -supermagic if there is a bijection such that and is constant over all subgraphs of which are isomorphic to . In this paper, we show that for odd and arbitrary , the firecracker is -supermagic, the banana tree is -supermagic and the flower is -supermagic.
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Taxonomy
TopicsGraph Labeling and Dimension Problems
