Computing F-index, coindex and Zagreb polynomials of the kth generalized transformation graphs

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 k th 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 k th generalized transformation graphs are obtained. Also, the Zagreb polynomials, Zagreb co-polynomials and their complements are computed.

On the Inverse Problem for Some Topological Indices

“…. , 15 e second hyper-Zagreb index of a tree (or molecular) graph can be any positive integer, except 2, 3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,28,29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,57,59,60,61,62,63,65,66,…”

“…e reformulated F-index of a tree (or molecular) graph can be any positive even integer, except for 4,6,8,12,14,16,20,22,28,30,36,38,46, 54, and 62.…”

“…In [26], Czabarka et al solved the IP for certain tree parameters. To study more about the inverse problems and the topological indices of graph operations, one can see these references [27][28][29][30][31][32].…”

Study of Generalized Hourglass Section in Carbon Nanocone via Connection Number

“…With the passage of time, the abovementioned quantities would be termed as the first and second Zagreb indices by many graph theorists and chemists. More than hundreds of researchers did work on it and published their work in highly reputed journals [7].…”

New Results on the Forgotten Topological Index and Coindex

“…In [20], some bounds were presented for the F-index and F-coindex. For more other bounds, see [21][22][23].…”