Abstract
Topological indices and connectivity polynomials are invariants of molecular graphs. These invariants have the tendency of predicting the properties of the molecular structures. The honeycomb network structure is an important type of benzene network. In the present article, new topological characterizations of honeycomb networks are given in the form of degree-based descriptors. In particular, we compute Zagreb and Forgotten polynomials and some topological indices such as the hyper-Zagreb index, first and second multiple Zagreb indices and the Forgotten index, F. We, for the first time, determine some regularity indices such as the Albert index, Bell index and I R M ( G ) index, as well as the F-index of the complement of the honeycomb network and several co-indices related to this network without considering the graph of its complement or even the line graph. These indices are useful for correlating the physio-chemical properties of the honeycomb network. We also give a graph theoretic analysis of some indices against the dimension of this network.
Highlights
Chemical graph theory relates the topology of hydrogen-depleted molecular graphs of chemical structures with physio-chemical properties
In 1988, Hosoya wrote another paper to elaborate the definition of W by proposing the Wiener polynomial, which, is known as the Hosoya polynomial according to Gutman
The degree-based topological index usually encodes important topological properties of the structure, which play a significant role in determining the physio-chemical properties of the molecules under discussion
Summary
Chemical graph theory relates the topology of hydrogen-depleted molecular graphs of chemical structures with physio-chemical properties. The authors in [5,6,7,8,9,10] computed the M-polynomial and related topological indices of nanostar dendrimers, titania and polyhex nanotubes, V-phenylenic nanotubes and nanotori, hex-derived networks and zigzag and rhombic benzenoid systems This polynomial is considered as the most general polynomial developed till and is rich in determining degree-based indices of molecular graphs. The degree-based topological index usually encodes important topological properties of the structure, which play a significant role in determining the physio-chemical properties of the molecules under discussion These indices are effectively utilized in quantitative structure-activity relationships (QSARs) and has many applications in risk assessment, toxicity prediction, regularity decisions, drug discovery and lead optimization [2,11,12,13]. New topological characterizations of the honeycomb network are given in the form of degree-based descriptors
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