On the antimagicness of generalized edge corona graphs.

Given a graph , a function of assigning distinct labels to such that , ∀ is an antimagic labeling of where indicates the vertex sum obtained by summing up all the labels assigned to the edges incident on the vertex . Let , , be connected graphs such that . A new graph is constructed from , , by adding all possible edges between the end vertices of and , .

A structural approach to the graceful coloring of a subclass of trees.

Let and be a simple graph. A graceful -coloring of is a proper vertex coloring of G using the colors in which leads to a proper edge coloring using colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromatic number .