Sharp Bounds of Kulli–Basava Indices in Generalized Form for k-Generalized Quasi Trees

Abstract

Molecular descriptors are a basic tool in the spectral graph, molecular chemistry, and various other fields of mathematics and chemistry. Kulli–Basava $\left(\mathbb{K}\mathfrak{B}\right)$ indices were initiated for chemical applications of various substances in chemistry. For simple graph $G$ , $\mathbb{K}\mathfrak{B}$ indices in generalized forms are $\mathbb{K}{\mathfrak{B}}_1^{\mathrm{\varrho }}\left(G\right)={{\displaystyle \sum }}_{gh\in E\left(G\right)}{\left({\mathbb{S}}_e\left(g\right)+{\mathbb{S}}_e\left(h\right)\right)}^{\mathrm{\varrho }}$ and $\mathbb{K}{\mathfrak{B}}_2^{\mathrm{\varrho }}\left(G\right)={{\displaystyle \sum }}_{gh\in E\left(G\right)}{\left({\mathbb{S}}_e\left(g\right).{\mathbb{S}}_e\left(h\right)\right)}^{\mathrm{\varrho }}$ , where ${\mathbb{S}}_e\left(\right)$