Lehmer 3 –Mean Labeling of Some New Disconnected Graphs

T.S.Pavithra; S.S.Sandhya; S.Somasundaram

doi:https://doi.org/10.14445/22315373/IJMTT-V35P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 1 | Year 2016 | Article Id. IJMTT-V35P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P501

Lehmer 3 –Mean Labeling of Some New Disconnected Graphs

T.S.Pavithra , S.S.Sandhya , S.Somasundaram

Citation :

T.S.Pavithra , S.S.Sandhya , S.Somasundaram, "Lehmer 3 –Mean Labeling of Some New Disconnected Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 1, pp. 1-14, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P501

Abstract

A graph G=(V,E) with P vertices and q edges is called Lehmer -3 mean graph ,if it is possible to label vertices x ЄV with distinct label f(x) from 1,2,3,………….q+1 in such a way that when each edge e=uv is labeled with f(e=uv)= 𝑓(𝑢) 3+𝑓(𝑣) 3 𝑓(𝑢) 2+𝑓(𝑣) 2 (or) 𝑓(𝑢) 3+𝑓(𝑣) 3 𝑓(𝑢) 2+𝑓(𝑣) 2 , then the edge labels are distinct. In this case f is called Lehmer -3 mean labeling of G. In this paper we investigate Lehmer -3 mean labeling of some standard graphs

Keywords

Graph, Path, Cycle, Comb, Crown, Ladder.

References

[1] J.A Gallian 2010, A dynamic survey of graph labeling. The electronic journal of combinatorics 17 # DS6
[2] Harary.F 1988 Graph theory, Narosa Publication House reading, New Delhi
[3]S Somasundram and R Ponraj 2003 Mean labeling of Graphs, National Academy of Science Letter Vol 26 (2013), p210-213
[4] S Somasundaram and R Ponraj and S SSandhya „Harmonic mean labeling of graphs‟ communicated to journal of combinatorial mathematics and combinatorial computing.
[5]S.Somasundaram, S.S.Sandhya and T.S.Pavithra, “Lehmer-3 Mean `Labeling of graphs” communicated to International Journal of Mathematical Forum
[6] S.SomasundaramS.S.Sandhya and T.S.Pavithra, “Some More Results On Lehmer-3 Mean Labeling of graphs” communicated to Global Journal of Theoretical and applied Mathematical Sciences.
[7] S.Somasundaram, S.S.Sandhya and T.S.Pavithra, “Some Results on Lehmer-3 Mean `Labeling of graphs” communicated to Journal of Discrete Mathematics and Cryptography.
[8] Jeyasekaran.C, Sandhya.S.S and David Raj.C “Some Results on Super Harmonic Mean Graphs”, International Journal of Mathematics Trends & Technology, Vol 6 (3) (2014), 215-224
[9] S.S Sandhya, E. Ebin Raja Merly, B Shiny, “ Super Geometric Mean labeling on Double Triangular Snakes” International Journal of Mathematics Trends & Technology, Volume 17 Number 1 – Jan 2015.