Multiplicative Wiener Index of Some Graphs

S.S. Sandhya; P.S. Akhshaya

doi:https://doi.org/10.14445/22315373/IJMTT-V70I4P106

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 70 | Issue 4 | Year 2024 | Article Id. IJMTT-V70I4P106 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I4P106

Multiplicative Wiener Index of Some Graphs

S.S. Sandhya, P.S. Akhshaya

Received	Revised	Accepted	Published
28 Feb 2024	24 Mar 2024	14 Apr 2024	30 Apr 2024

Abstract

The Multiplicative Wiener Index, 𝜋(𝐺), is equal to the product of distance between all the pairs of vertices of G. In this paper, we investigate the Multiplicative Wiener Index of some standard graphs, which satisfies Harmonic Mean labeling.

Keywords

Graph, Harmonic Mean graphs, Path, Triangular snake graph, Comb graph, Hurdle graph, Friendship graph.

References

[1] Joseph A. Gallian, “A Dynamic Survey of Graph Labeling,” The Electronic Journal of Computations, 2018.
[Google Scholar] [Publisher Link]
[2] Frank Harary, Graph Theory, Addison-Wesley Publishing Company, pp. 1-274, 1969.
[Publisher Link]
[3] S.S. Sandhya and S. Somasundaram, “Harmonic Mean Labeling for Some Special Graphs,” International Journal of Mathematics Research, vol. 5, no. 1, pp. 55-64, 2013.
[Google Scholar] [Publisher Link]
[4] Ivan Gutman et al., “The Multiplicative Version of the Wiener Index,” Journal of Chemical Information & Computer Sciences, vol. 40, pp. 113-116, 2000.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Ivan Gutman et al., “On the Multiplicative Wiener Index and Its Possible Chemical Applications,” Chemical Monthly, vol. 131, pp. 421- 427, 2000.
[CrossRef] [Google Scholar] [Publisher Link]
[6] S. Somasundaram, and R. Ponraj, “Mean Labeling of Graphs,” National Academy of Science Letters, vol. 26, pp. 210-213, 2003.
[7] Harry Wiener, “Structural Determination of the Paraffin Boiling Points,” Journal of the American Chemical Society, vol. 69, pp. 17-20, 1947.
[CrossRef] [Google Scholar] [Publisher Link]

Citation :

S.S. Sandhya, P.S. Akhshaya, "Multiplicative Wiener Index of Some Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 4, pp. 45-50, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I4P106