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 K B indices were initiated for chemical applications of various substances in chemistry. For simple graph G , K B indices in generalized forms are K B 1 ϱ G = ∑ g h ∈ E G S e g + S e h ϱ and K B 2 ϱ G = ∑ g h ∈ E G S e g . S e h ϱ , where S e g = ∑ e ∈ N e g d G e , and for edge e = g , h , the degree is d G e = d G g + d G h − 2 and ϱ ≠ 0 is any real number. The graph G is said to be a k − g e n e r a l i z e d quasi tree if for the vertex set U k ⊂ G having U k = k , G − U k is a tree and for U k − 1 ⊂ V G having U k − 1 = k − 1 , G − U k − 1 is not a tree. In this research work, we have successfully investigated sharp bounds of generalized K B 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.