Further results on Odd Super Graceful Labeling of Graphs

Document Type : Primary Research paper


Department of Mathematics, Maharani’s Science College for Women, Mysore-570 005, Karnataka, INDIA.


A graph ๐‘ฎ with ๐’‘ vertices and ๐’’ edges is said to have an odd super graceful labeling if there exists an injective function ๐’‡:๐‘ฝ(๐‘ฎ)∪๐‘ฌ(๐‘ฎ)→{๐Ÿ,๐Ÿ,๐Ÿ‘,…,๐’‘+๐’’} such that ๐’‡(๐’–๐’—)=|๐’‡(๐’–)−๐’‡(๐’—)|, for all ๐’–๐’—∈๐‘ฌ(๐‘ฎ) and all its vertex labels are odd. A graph that admits an odd super graceful labeling is called an odd super graceful graph. In this paper, we investigate the odd super gracefulness of some graphs obtained by graph operations such as identification, carona, vertex duplication and edge duplication.