  An antimagic labeling of a graph $G$ is a one-to-one correspondence between
the edge set $E(G)$ and $\lbrace 1,2,...,|E(G)|\rbrace$ in which the sum of the
edge labels incident on the distinct vertices are distinct. Let
$G$,$H_1$,$H_2$,...,$H_{m-1}$, and $H_m$ be simple graphs where $|E(G)|=m$. A
generalized edge corona of the graph $G$ and $(H_1,H_2,...,H_m)$ (denoted by
$G\diamond (H_1,H_2,...H_m)$) is a graph obtained by taking a copy of
$G,H_1,H_2,...,H_m$ and joining the end vertices of $i^{th}$ edge of $G$ to
every vertex of $H_i$, $i\in\lbrace 1,2,...,m\rbrace$. In this paper, we
consider $G$ as a connected graph with exactly one vertex of maximum degree 3
(excluding the spider graph with exactly one vertex of maximum degree 3
containing uneven legs) and each $H_i$, $1\leq i \leq m$ as a connected graph
on at least two vertices. We provide an algorithmic approach to prove that $G$
$\diamond$ $(H_1,H_2,...H_m)$ is antimagic under certain conditions.
