Elegant Labeling of Some Graphs

Abstract

An elegant labeling on graph G with vertices and edges is an injective (one-to-one) mapping from the set of vertices V (G) to the set of non-negative integers f0; 1; 2; 3; :::; g in such a way that the set of values on the edges obtained by the sums mod + 1 of the labels of their end vertices is f1; 2; 3; 4; : : : ; g. The purpose of this research is to prove that several graphs, namely diamond ladder admit an elegant labeling. We also look for relationships between Edge Antimagic Vertex Labeling and Elegant Labeling.