Abstract
In chemical graph theory, forgotten topological index or F-index plays a crucial role to collect information about the properties of chemical compounds. The kth generalized transformation graphs of a molecular graph preserve the entire information on the molecular topology contained in the relevant molecular graph. In this paper, some exact expressions of the F-index and its co-index for the kth generalized transformation graphs are obtained. Also, the Zagreb polynomials, Zagreb co-polynomials and their complements are computed.
Highlights
Chemical compounds are often used to model different molecular structures which are graphically represented as molecular graphs in which atoms as nodes and chemical bonds as edges
We present some explicit expressions for the F -index of the kth generalized transformation graphs of a molecular graph in terms of various graph invariants
Some figures are constructed to show their changes under different kth generalized transformation graphs
Summary
Chemical compounds are often used to model different molecular structures which are graphically represented as molecular graphs in which atoms as nodes and chemical bonds as edges. Index in [3] is calculated as the sum of the power three of degrees of the vertices of a graph. It is further found in Furtula et al in [5]. On the base of Zagreb coindices, Basavanagoud and Jakkannavar [13] defined three new graph polynomials, namely the first, second and third Zagreb co-polynomials.
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