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Inverse Sum Indeg Index of Subdivision, t-Subdivision Graphs, and Related Sums

Inverse Sum Indeg Index of Subdivision, t-Subdivision Graphs, and Related Sums
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Author(s): Amitav Doley (DHSK College, India), Jibonjyoti Buragohain (Dibrugarh University, India) and A. Bharali (Dibrugarh University, India)
Copyright: 2020
Pages: 16
Source title: Handbook of Research on Advanced Applications of Graph Theory in Modern Society
Source Author(s)/Editor(s): Madhumangal Pal (Vidyasagar University, India), Sovan Samanta (Tamralipta Mahavidyalaya, India) and Anita Pal (National Institute of Technology Durgapur, India)
DOI: 10.4018/978-1-5225-9380-5.ch005

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Abstract

The inverse sum indeg (ISI) index of a graph G is defined as the sum of the weights dG(u)dG(v)/dG(u)+dG(v) of all edges uv in G, where dG(u) is the degree of the vertex u in G. This index is found to be a significant predictor of total surface area of octane isomers. In this chapter, the authors present some lower and upper bounds for ISI index of subdivision graphs, t-subdivision graphs, s-sum and st -sum of graphs in terms of some graph parameters such as order, size, maximum degree, minimum degree, and the first Zagreb index. The extremal graphs are also characterized for their sharpness.

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