Abstract

On Hyper-Zagreb Index of Three Graph Operations

A. Bharali1 and Amitav Doley2

1Department of Mathematics, Dibrugarh University-786004, INDIA. 2Department of Mathematics, DHSK College, Dibrugarh-786004, INDIA.

ABSTRACT

The Hyper-Zagreb index of a graph 𝐺= (𝑉,𝐸) is defined as 𝐻𝑍(𝐺)=Σ[𝑑𝐺(𝑎)+𝑑𝐺(𝑏)]2𝑎𝑏𝜖𝐸 , where 𝑑𝐺(𝑢) is the degree of the vertex 𝑢 in 𝐺. In this paper, some explicit expressions of the Hyper-Zagreb index and its coindices of the tensor product of n graphs, strong product of graphs and semi-strong product of graphs are derived. Mathematics Subject Classification (2010): 05C76, 05C07.

Keywords :Hyper-Zagreb index, Hyper-Zagreb coindices, Tensor product, Strong product, Semi-strong product.

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