On the antimagicness of generalized edge corona graphs.

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