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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 4 | Year 2020 | Article Id. IJMTT-V66I4P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I4P504

Harmonic Mean Labeling Of Zig-Zag Triangle graphs


S.Meena, M.Sivasakthi.
Abstract

A graph G with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertixnodes XεV with distinct labels f(x) from { 1,2....q+1} in such a way that each edge e=uv is labeled with f(uv) = [2f(u)f(v)/f(u)+f(v)] or [2f(u)f(v)/f(u)+f(v)] then the edge labels are distinct. In this case f is called Harmonic mean labeling of G. In this paper we prove that some families of graphs such as zig-zag triangle of Z(Tn)⊙K1, Z(Tn)⊙ K bar2, Z(Tn)⊙K2, are harmonic mean graphs.

Keywords
Harmonic mean graph, zig-zag triangle of Z(Tn)⊙ K1, Z(Tn)⊙ K bar2, Z(Tn)⊙ K2.
References

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[4] S.Meena, M.Renugha,M.Sivasakthi, “Cardial Labeling For Different Type Of Shell Graphs” International Journal Of Scientific and Engineering Research, Vol.No.6,Issue 9,Sep 2015.
[5] S.Meena, M.Sivasakthi, “Harmonic Mean Labeling Subdivision Graphs” International Journal Of Research And Analytical Reviews,Volume 6, Issue 1, Jan-March2019,E-ISSN 2348-1269, P-ISSN 2349-5138.
[6] S.Meena, M.Sivasakthi, “Some Results On Harmonic Mean Graphs” International Journal Of Research And Analytical Reviews,Volume 6, Issue 2, June 2019,E-ISSN 2348-1269, P-ISSN 2349-5138.
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[8] S.S. Sandhya, S.Somasundaram and R.Ponraj , “ Harmonic Mean Labeling of Some Cycle Related Graphs”Internation Journal Of Math.Analysis,vol.6,2012, No.40, PP-1997-2005.
[9] S.S. Sandhiya, S.Somasundaram and R.Ponraj , “Some More Result On Harmonic Mean Graphs”, Journal Of Mathematics Research,vol.4,Feb(2012),No.1 Pg: 21– 29.
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[11] S.S.Sandhya, C.David raj, and C.Jayasekaran, “Some New Results On Harmonic Mean Graphs”,International Journal Of Mathematical Archive-4(5), (2013) Pg 240-245

Citation :

S.Meena, M.Sivasakthi., "Harmonic Mean Labeling Of Zig-Zag Triangle graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 4, pp. 17-27, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I4P504

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