Prime Graceful Labeling
Abstract
A graph G with m vertices and n edges, is said to be prime graceful labeling, if there is an injection from the vertices of G to {1, 2, ..., k} where k = min {2m, 2n} such that gcd ( ( ), ( )=1 and the induced injective function from the edges of G to {1, 2, ..., k − 1} defined by ( ) = | ( ) − ( ) | , the resulting edge labels are distinct. In this paper path , cycle Cn , star K1,n , friendship graph Fn , bistar Bn,n, C4 ∪ Pn , Km,2 and Km,2 ∪ Pn are shown to be Prime Graceful Labeling .
About this article
Keywords
- Prime labeling
- graceful labeling and prime graceful labeling.
References
[1] Tout R, Dabboucy AN & Howalla K, “Prime labeling of graphs”, National Academy Science Letters-India, Vol.5, No.11, (1982), pp.365-368.
[2] Harary F, Graph Theory, Addison-Wesley, Reading, Mass, (1969).
[3] Bondy JA & Murthy USR, “Graph theory with applications”, Elsevier North Holland. New York, (1976).
[4] Gallian JA, “A dynamic survey of graph labeling”, The electronic journal of combinatory, Vol.16, No.6, (2009), pp.1-219.
[5] Rosa A, “On certain valuations of the vertices of a graph”, Theory of Graphs (Internet Symposium, Rome, (1966), pp.349-355.
[6] Uma R & Murugesan, N, “Graceful labeling of some graphs and their sub graphs”, Asian Journal of Current Engineering and Maths, Vol.1, No.6, (2013), pp.307-370.
[7] Vaidya SK & Vihol PL, “Prime cordial labeling for some cycle related graphs”, International Journal of Open Problems in Computer Science and Mathematics, Vol.3, No.5, (2010), pp.98-104.
[8] Vaidya SK & Shah NH, “Graceful and odd graceful labeling of some graphs”, International journal of Mathematics and soft computing, Vol.3, No.1, (2013), pp.61-68.
[9] Singhun S, “Graphs with line-odd Graceful labeling”, International Mathematics Forum, Vol.8, No.12, (2010), pp.577-582.
[10] Sridevi R, Navaneethakrishnan S & Nagarajan K, “Super Fibonacci graceful labeling of some special class of graphs”, Mathematical Combinatory, Vol.1, (2011), pp.59-72.