On the antimagicness of generalized edge corona graphs

Given a graph.., a function of assigning distinct labels {1, 2,..., |E(G)|} to E(G) such that w(a) not equal w(b), for all a, b is an element of V(G) is an antimagic labeling of G where w(a) indicates the vertex sum obtained by summing up all the labels assigned to the edges incident on the vertex a. Let G, H-t, 1 <= i <= m be connected graphs such that E(G) = {e(1), e(2), ..., e(m)}. A new graph is constructed from G, H-i, 1 <= i <= m by adding all possible edges between the end vertices of e(i) and V(H-i), i is an element of{H-1, H-2, ..., H-m}. The resulting graph is called the generalized edge corona of G and (H-1, H-2, ..., H-m) which is denoted as G lozenge (H-1, H-2, ..., H-m). We prove G lozenge (H-1, H-2, ..., H-m). 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 |V (H-i)| >= 2, i is an element of{1, 2,..., m}.