Antimagic labeling graphs with a regular dominating subgraph

An antimagic labeling of a connected graph with ℓ   edges is an injective assignment of labels from {1,…,ℓ}{1,…,ℓ} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K2K2 has an antimagic labeling. Motivated by a result of Barrus for split graphs we prove the conjecture for graphs with a regular dominating subgraph.

► We proved conjecture for graphs with a regular dominating subgraph.
► Firstly we show steps how to label a graph.
► Then we show that the described way of labeling is antimagic.