Perfectly antimagic total labeling of star-like trees and the corona product of two graphs

Abstract

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.)