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 KB indices were initiated for chemical applications of various substances in chemistry. For simple graph G, KB indices in generalized forms are KB1ϱG=∑gh∈EGSeg+Sehϱ and KB2ϱG=∑gh∈EGSeg.Sehϱ, where Seg=∑e∈NegdGe, and for edge e=g,h, the degree is dGe=dGg+dGh−2 and ϱ≠0 is any real number. The graph G is said to be a k−generalized quasi tree if for the vertex set Uk⊂G having Uk=k, G−Uk is a tree and for Uk−1⊂VG having Uk−1=k−1, G−Uk−1 is not a tree. In this research work, we have successfully investigated sharp bounds of generalized KB indices for k-generalized quasi trees where ϱ≥1. Chemical applications of the generalized form are also studied for alkane isomers with scatter diagrams and residuals.