Anti-magic Labeling of Cartoon Flowers and Consecutive Wounded Flowers

Abstract

An anti-magic labeling of a finite simple undirected graph G is a bijection from the set of edges to the set of integers {1, 2,…, |E(G)|} such that the vertex sums are pairwise distinct, where the vertex sum at one vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an anti-magic labeling. In this paper, we established an anti-magic labeling of the cartoon flowers. We further define a new subclass of the cartoon flower called the consecutive wounded cartoon flower and then established an anti-magic labeling of the consecutive wounded cartoon flowers.