On the antimagicness of generalized edge corona graphs

Given a graph G, a function of assigning distinct labels $$ to $$ such that $$, ∀ $$ is an antimagic labeling of G where $$ indicates the vertex sum obtained by summing up all the labels assigned to the edges incident on the vertex a. Let G, $$, $$ be connected graphs such that $$. A new graph is constructed from G, $$, $$ by adding all possible edges between the end vertices of $$ and $$, $$. The resulting graph is called the generalized edge corona of G and $$ which is denoted as $$. We prove G ⋄ $$ is antimagic under certain conditions using an algorithmic approach where G has only one vertex of maximum degree three (excluding spider graphs containing uneven legs) and $$, $$.