eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences August 2010 22 2 407 412 jusps-A 987 article S. Venkatesan 1 R. Sattanathan 2 Research Scholar, Dravidian University Reader & Head PG & Research, Deptt. of Mathematics D.G. Vaishnav College, (Autonomous) Chennai (INDIA) <p style="text-align: justify;">Graceful labeling is assignment of distinct labels from <em>f {0</em>,&hellip;., |<em>E|} </em>to vertices of graph, where edges are labeled by difference of absolute values of adjacent vertices and every label from <em>f {1,2</em>,&hellip;.,|<em>E|} </em>is used exactly once as an edge label. The edge gracefulness is reversal of gracefulness. It involves labeling edges, rather than vertices, with an induced numbering consisting of sums of edge- labels, rather than differences of vertex labels. It is still not known, if every tree has a graceful labeling. In this paper, we are discussing about the edge graceful labeling of bicycle graphs and its uniqueness.</p> <p style="text-align: justify;">&nbsp;</p> https://www.ultrascientist.org/paper/987/ graph labeling graceful labeling edge - graceful labeling bicycle graph