Abstract
Graceful labeling of graphs is used in radar codes. In this work, we introduce a new version of gracefulness we call it edge even graceful labeling of graphs. A necessary and sufficient condition for edge even graceful labeling of path graph, P-n,P- cycle graph, C-n, and star graph 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.