Super Fibonacci Gracefulness of Shell Related Graphs

D.Amuthavalli; M.Sangaeetha

doi:https://doi.org/10.14445/22315373/IJMTT-V53P552

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 6 | Year 2018 | Article Id. IJMTT-V53P552 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P552

Super Fibonacci Gracefulness of Shell Related Graphs

D.Amuthavalli, M.Sangaeetha

Abstract

A graph is said to be Super Fibonacci graceful if the function 𝑓 is defined as 𝑓: 𝑉(𝐺) ⟶ {0, 𝐹1 , 𝐹2 , … , 𝐹𝑞 } and the induced edge labeling 𝑓 ∗ ∶ 𝐸(𝐺) ⟶ {𝐹1 , 𝐹2 , 𝐹3 , … , 𝐹𝑞 } defined as 𝑓 ∗ (𝑢𝑣) = 𝑓(𝑢)− 𝑓(𝑣) is bijective. In this paper an analysis is made on Shell, Shell-flower and Bow graphs under Super Fibonacci graceful graphs.

Keywords

Labeling, Super Fibonacci graceful labeling, Shell, Shell-flower graph, Bow graph.

References

[1] David.W and Anthony.E.Barakaukas, “Fibonacci graceful graphs”.
[2] Harary.F, “Graph Theory”, Narosa Publishing House (2001).
[3] Joseph A. Gallian, “A Dynamic survey of graph labeling”, the electronic journal of combinatorics,(2013).
[4] Jeba Jesintha .J. Ezhilarasi Hilda Stanley “ Graceful labeling of Bow graphs and Shell-flower graphs”
[5] Kathiresan K. and Amutha S., Fibonacci graceful graphs, Ph.D. Thesis, Madurai Kamaraj University, (October 2006).
[6] Murugesan. N and Uma. R, “A conjecture on amalgation of graceful graphs star graphs”, Int. J. Cont. Math. Science,Vol.7,(2012).
[7] Rosa.A, “On certain valuation of vertices of graph”,(1967).
[8] D.Amuthavalli “Super Fibonacci graceful labeling of some cycle related graphs”,Int. J. Mathematics Trends and Technology.(2016).

Citation :

D.Amuthavalli, M.Sangaeetha, "Super Fibonacci Gracefulness of Shell Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 6, pp. 424-430, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P552