New Algorithms on E-Super (a, d)-edge-antimagic Graceful labeling

Abstract

An E-super (a, d)-edge-antimagic graceful labeling (EEAGL) is a one-one and onto function λ from the union of the vertex set and edge set of G into the integers from 1 to p + q where P is the total number of vertices. The absolute value of λ(u) + λ(v) - λ(uv), uv in G consists of integers from a to a + (q-1) d which are consecutive with a, the initial term and d, the common difference. If the edge-weights of the graph G are labeled by the integers from 1 to q then the labeling is named as EEAGL. In this paper, we prove the above labeling for the disjoint union of multiple copies (DUMC) of cycle graphs, complete graphs and path graphs. Finally, we construct algorithms to find some classes of graphs are EEAGL.