On Harmonic Index of New Operation of Graphs
S.Uma1, N. Velmurugan2
1S.Uma, Department of Mathematics, Government Arts College for Women, Mayiladuthurai (Tamil Nadu), India.
2N.Velmurugan, Department of Mathematics, Theivannai Ammal College for Women Autonomous Villupuram (Tamil Nadu), India.
Manuscript received on 29 May 2019 | Revised Manuscript received on 11 June 2019 | Manuscript Published on 22 June 2019 | PP: 873-877 | Volume-8 Issue-3S, February 2019 | Retrieval Number: C11850283S19/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: The harmonic index of a graph , denoted by H(), is defined as H()= 𝟐 𝑫𝒈(𝒓)+𝑫𝒈(𝒔) 𝒓𝒔∈𝑬() where 𝑫𝒈(𝒓) is the drgree of a vertex r in . In this paper , we concentrate the upper bounds of the harmonic index for four types of derived graphs.
Keywords: Harmonic Index, Join, Subdivision, Total Graph. MSC: 05C12, 05C76.
Scope of the Article: Cryptography and Applied Mathematics