Skolem difference Fibonacci mean labelling of
some special class of graphs

L. Meenakshi sundaram; A. Nagarajan

doi:https://doi.org/10.14445/22315373/IJMTT-V39P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 39 | Number 2 | Year 2016 | Article Id. IJMTT-V39P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P512

Skolem difference Fibonacci mean labelling of some special class of graphs

L. Meenakshi sundaram, A. Nagarajan

Abstract

The concept of Skolem difference mean labelling was introduced by K. Murugan and A. Subramanian[6]. The concept of Fibonacci labelling was introduced by David W. Bange and Anthony E. Barkauskas[1] in the form Fibonacci graceful. This motivates us to introduce skolem difference Fibonacci mean labelling and is defined as follows: “A graph G with p vertices and q edges is said to have Skolem difference Fibonacci mean labelling if it is possible to label the vertices x∈ V with distinct elements f(x) from the set {1,2,...,Fp+q} in such a way that the edge e = uv is labelled with|( f(u)-f(v))/2| if |f(u)-f(v)| is even and (|f(u)-f(v)|+1)/2 if |f(u)-f(v)| is odd and the resulting edge labels are distinct and are from {F1, F2,...,Fq}. A graph that admits Skolem difference Fibonacci mean labelling is called a Skolem difference Fibonacci mean graph”. In this paper, we prove that some special class of graphs are Skolem difference Fibonacci mean graphs.

Keywords

Skolem difference mean labelling, Fibonacci labelling, Skolem difference Fibonacci mean labelling, Fan Fn, Fm @ 2Pn, triangular snake graph TSn, 〖rP〗_(n )∪ 〖sP〗_m, ⋃_(i=2)^n▒P_i.

References

[1] David W. Bange and Anthony E. Barkauskas, “Fibonacci graceful graphs” (1980).
[2] Harary, Graph Theory, Addison Welsley (1969).
[3] J.A.Bondy and U.S.R.Murthy, “Graph Theory and Applications” (North-Holland), Newyork, 1976.
[4] J.A.Gallian, A Dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 18(2014), #DS6.
[5] Kathiresan K. and Amutha S., Fibonacci graceful graphs, Ph.D. Thesis, Madurai Kamaraj University, (October 2006).
[6] K. Murugan and A. Subramanian, Skolem difference mean labelling of H- graphs, International Journal of Mathematics and Soft Computing, Vol.1, No. 1, (August 2011), p115-129.
[7] L. Meenakshi sundaram and A. Nagarajan, Skolem difference Fibonacci mean labelling of standard (communicated).
[8] L. Meenakshi sundaram and A. Nagarajan, Skolem difference Fibonacci mean labelling of special class of trees (communicated).
[9] L. Meenakshi sundaram and A. Nagarajan, Skolem difference Fibonacci mean labelling of H- class of graphs (communicated).
[10] L. Meenakshi sundaram and A. Nagarajan, Skolem difference Fibonacci mean labelling of path related graphs (communicated).

Citation :

L. Meenakshi sundaram, A. Nagarajan, "Skolem difference Fibonacci mean labelling of some special class of graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 2, pp. 88-93, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P512