Antimagic labeling of <i>n</i> -uniform cactus chain graphs

A graph [Formula: see text] is considered antimagic if it admits antimagic labeling. The antimagic labeling of a finite, simple graph with [Formula: see text] and [Formula: see text] is a bijective function from the set of edges to the set of integers [Formula: see text] such that the vertex sum of [Formula: see text] vertices is pairwise distinct. The vertex sum of a vertex is obtained by summing the labels of all edges incident to it. Hartsfield and Ringel conjectured that every connected graph different from [Formula: see text] is antimagic. Supporting this conjecture, it was shown that the dense graphs are antimagic. A cactus graph is a connected graph where no edge lies within more than one cycle. A cactus graph in which each block is a cycle of the same size [Formula: see text] is called an n-uniform cactus graph. We proved that Hartsfield and Ringel’s conjecture is true for [Formula: see text]-uniform cactus chain graphs with and without pendant vertices, which are specific cases of sparse graphs.