New Classes of Harmonic Mean Graphs

S.S.Sandhya; S. Somasundaram

doi:https://doi.org/10.14445/22315373/IJMTT-V22P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 22 | Number 1 | Year 2015 | Article Id. IJMTT-V22P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V22P501

New Classes of Harmonic Mean Graphs

S.S.Sandhya, S. Somasundaram

Citation :

S.S.Sandhya, S. Somasundaram, "New Classes of Harmonic Mean Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 22, no. 1, pp. 1-8, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V22P501

Abstract

A Graph G = (V, E) with p vertices and q edges is said to be Geometric mean graph if it is possible to label the vertices x V with distinct labels f(x) from 1,2,….q+1 in such a way that when each edge e=uv is labeled with f(e=uv) = then the resulting edge labels are distinct. In this case f is called Harmonic mean labeling of G. In this paper, we investigate Harmonic mean labeling for path and cycle related graphs.

Keywords

Graph, Path, Cycle, Harmonic mean labeling, Shadow graph, Splitting graph, Middle graph and Total graph.

References

[1] J.A.Gallian, A dynamic survey of graph labeling. The Electronic Journal of combinators 17#DS6.
[2] F.Harary, Graph theory, Narosa publishing House New Delhi.
[3] S. Somasundram and R.Ponraj, Mean labeling of graphs, National Academy of Science letters vol.26, p210-2013
[4] S.S.Sandhya,and S. Somasundaram, Harmonic mean labeling of graphs International Journal of Mathematics Research vol.6, No.2(2014) pp179-182.