Edge Antimagic Total Labeling on Paths and Unicycles

Let \( G = (V, E) \) be a simple and undirected graph with \( v \) vertices and \( e \) edges. An \( (a, d) \)-\emph{edge-antimagic total labeling} is a bijection \( f \) from \( V(G) \cup E(G) \) to the set of consecutive integers \( \{1, 2, \dots, v + e\} \) such that the weights of the edges form an arithmetic progression with initial term \( a \) and common difference \( d \). A super \( (a, d) \)-\emph{edge antimagic total labeling} is an edge antimagic total labeling \( f \) such that \( f(V(G)) = \{1, \dots, v\} \). In this paper, we solve some problems on edge antimagic total labeling, such as on paths and unicyclic graphs.