Computing FGZ Index of Sum Graphs under Strong Product
Abstract: Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related operations and strong product of graphs which create hexagonal chains isomorphic to many chemical compounds. Mainly, the exact values of first general Zagreb index (FGZI) for four sum graphs are obtained. At the end, FGZI of the two particular families of sum gra… Show more
Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Cited by 4 publications
References 27 publications
A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H . For D ∈ S , R , Q , T and the connected graph H , the derived graphs D H are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph ( D -sum graph) is obtained by the Cartesian product of the graph H 2 with the graph D H 1 . In this study, we compute forgotten coindex of the D -sum graphs H 1 + S H 2 ( S -sum), H 1 + R H 2 ( R -sum), H 1 + Q H 2 ( Q -sum), and H 1 + T H 2 ( T -sum) in the form of various indices and coindices of the factor graphs H 1 and H 2 . At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D -sum graphs.
A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H . For D ∈ S , R , Q , T and the connected graph H , the derived graphs D H are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph ( D -sum graph) is obtained by the Cartesian product of the graph H 2 with the graph D H 1 . In this study, we compute forgotten coindex of the D -sum graphs H 1 + S H 2 ( S -sum), H 1 + R H 2 ( R -sum), H 1 + Q H 2 ( Q -sum), and H 1 + T H 2 ( T -sum) in the form of various indices and coindices of the factor graphs H 1 and H 2 . At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D -sum graphs.
In theoretical chemistry, topological indices (TIs) have important role to predict various physical and structural properties of the study under molecular graphs. Among all topological indices, Zagreb-type indices have been used more effectively in the chemical literature. In this paper, we have computed first Zagreb, second Zagreb, forgotten, and hyper Zagreb indices of the generalized Q -sum graph H 1 Q α H 2 in the form of different TIs of its basic graphs, where α ≥ 1 is a positive integer. This family of graphs is obtained by the lexicographic product of the graph Q α H 1 and H 2 , where Q α H 1 is constructed with the help of the generalized line superposition operation Q α on H 1 . As a conclusion, we also checked the correlation between predefined graph H 1 H 2 under the operation of lexicographic product H 1 and H 2 with newly defined generalized Q -sum graphs H 1 Q α H 2 using linear regression models of various degree-based TIs.
The valency based topological indices (TIs) are defined by algebraic functions as the chemical graph theory tools in which the structural parameters are used as input and the output is related with the topology of chemical species. In theoretical chemistry, the TIs are mainly used to investigate/develop the QSAR and QSPR investigations of the molecular graphs. The Reformulated F-index or RFI is one such kind of TIs. The RFI for a molecular graph Y is defined as R F Y = ∑ u v ∈ E Y d Y u + d Y v − 2 3 , where d Y u is the degree of a vertex u in Y . In this paper, we study the RFI for vertex and edge version of F-join of given general graphs which are related to subdivision and total graph.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
Contact Info
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Product
Resources
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.
