Edge Even Graceful Labeling of Some Path and Cycle Related Graphs

Abstract

Graceful labeling of graphs is used in radar codes. In this work, we introduce a new version of gracefulness, which we call edge-even graceful labeling of graphs. We establish a necessary and sufficient condition for edge-even graceful labeling of path graphs \(P_n\), cycle graphs \(C_n\), and star graphs \(K_{1,n}\). We also prove some necessary and sufficient conditions for some path and cycle-related graphs, namely, Friendship, Wheel, Double wheel, and Fan graphs.