2024

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M-POLYNOMIAL BASED MATHEMATICAL FORMULATION OF THE (a, b)-NIRMALA INDEX AND ITS BOUNDS
(Palestine Polytechnic University, 2024) Shibsankar Das; Shikha Rai
Topological indices are graph-invariant numerical parameters that characterize the topology of a graph. Numerous topological indices have been developed and many of them have played an essential role in forecasting the chemical, pharmacological, and other characteristics of molecular graphs. In early 2022, a new topological index was introduced depending on the degree of end vertices of an edge in a graph and was named the (a, b)-Nirmala index. In this paper, we formulate the (a, b)-Nirmala index in terms of M-polynomial of a graph χ and present its correlation with several related previously defined well-known degree-dependent topological indices of χ. Moreover, we derive the value of the (a, b)-Nirmala index for some standard graphs. Additionally, we determine some general bounds for the (a, b)-Nirmala index of χ. © Palestine Polytechnic University-PPU 2024.