Antimagic total labeling on a class of acyclic graphs
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Date
2019
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UMT Lahore
Abstract
Let (G = (V(G), E(G))) be a simple graph with finite vertex set (V(G)) and edge set (E(G)) as a two-element subset of (V(G)). Precisely, a mapping ( \phi : V(G) \cup E(G) \to {1,2,3,\dots,v+e} ) is called an ((a,d))-edge antimagic total labeling if the set ( {\phi(u)+\phi(v)+\phi(uv) : uv \in E(G)} ) forms an arithmetic progression with first term (a) and common difference (d). Moreover, this labeling becomes super ((a,d))-edge antimagic total labeling if the vertices attain the smallest labels, i.e., (\phi(V(G)) = {1,2,3,\dots,v}). In this thesis, we prove the results related to the super ((a,d))-edge antimagic total labeling of a class of acyclic graphs under certain conditions.