Antimagic labeling of n-uniform cactus chain graphs

A graph G = (V,E) is considered antimagic if it admits antimagic labeling. The antimagic labeling of a finite, simple graph with |V | = n and |E| = m is a bijective function from the set of edges to the set of integers {1, 2,& mldr;,m} such that the vertex sum of n 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 K2 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 n is called an n-uniform cactus graph. We proved that Hartsfield and Ringel's conjecture is true for n-uniform cactus chain graphs with and without pendant vertices, which are specific cases of sparse graphs.