Geodesic
Perfectly antimagic total labeling of star-like trees and the corona product of two graphs
P. Swathi1 ; Ramasamy Jeyabalan1 ; P. Swathi ; Ramasamy Jeyabalan
1Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India
Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 2, pp. 95-100 
P. Swathi; Ramasamy Jeyabalan; P. Swathi; Ramasamy Jeyabalan. Perfectly antimagic total labeling of star-like trees and the corona product of two graphs. Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 2, pp. 95-100. http://geodesic.mathdoc.fr/item/AMUC_2024_93_2_a1/
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     title = { Perfectly antimagic total labeling of star-like trees and the corona product of two graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {95--100},
     year = {2024},
     volume = {93},
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     url = {http://geodesic.mathdoc.fr/item/AMUC_2024_93_2_a1/}
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A totally antimagic total labeling whose vertex and edge weights are also pairwise distinct is said to be a perfectly antimagic total labeling. A graph with this labeling is known as a perfectly antimagic total (PAT) graph. This paper discusses the possibility of the perfectly antimagic total labeling of a star-like trees. We also developed perfectly antimagic total labeling for the Corona product of path with $nK_1$ and cycle with $nK_1$ for all $n \geq 1$. Finally, we provide a particular solution to the open problem under total labeling on Antimagic labelings of caterpillars and Caterpillars are antimagic (Antoni Lozano et al.)