Conjugated tricyclic graphs with maximum variable sum exdeg index

Rizwan, Muhammad; Bhatti, Akhlaq Ahmad; Javaid, Muhammad; Shang, Yilun

doi:10.1016/j.heliyon.2023.e15706

Cited by 8 publications

(3 citation statements)

References 23 publications

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“…where f is a real-valued function. Some initial studies, recent developments, and a survey on the indices of the form (8) can be found in [23][24][25][26][27][28][29], respectively.…”

Section: Extremal Results Concerning Molecular ξ-Cyclic Graphsmentioning

confidence: 99%

Ad-Hoc Lanzhou Index

Ali,

Shang,

Dimitrov

et al. 2023

Mathematics

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This paper initiates the study of the mathematical aspects of the ad-hoc Lanzhou index. If G is a graph with the vertex set {x1,…,xn}, then the ad-hoc Lanzhou index of G is defined by Lz˜(G)=∑i=1ndi(n−1−di)2, where di represents the degree of the vertex xi. Several identities for the ad-hoc Lanzhou index, involving some existing topological indices, are established. The problems of finding graphs with the extremum values of the ad-hoc Lanzhou index from the following sets of graphs are also attacked: (i) the set of all connected ξ-cyclic graphs of a fixed order, (ii) the set of all connected molecular ξ-cyclic graphs of a fixed order, (iii) the set of all graphs of a fixed order, and (iv) the set of all connected molecular graphs of a fixed order.

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“…where f is a real-valued function. Some initial studies, recent developments, and a survey on the indices of the form (8) can be found in [23][24][25][26][27][28][29], respectively.…”

Section: Extremal Results Concerning Molecular ξ-Cyclic Graphsmentioning

confidence: 99%

Ad-Hoc Lanzhou Index

Ali,

Shang,

Dimitrov

et al. 2023

Mathematics

Self Cite

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“…The ZIs and RI, dependent on the ev-degree and ve-degree notations, are formulated in [26][27][28][29], and it was analysed that the predicting ability of ve-degree ZI was improved as compared to its classical version. Recently, the maximum variable exdeg index for conjugated tricyclic graphs [30], the Sombor index and degree-related properties of simplicial networks [31], a unified approach for extremal general exponential multiplicative ZIs [32] and the Gaussian Estrada index of graphs [33] are also notable additions to the study of TIs. For more developments on the study of TIs, see [34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

Rani,

Fahad,

Hussain

et al. 2023

Meas. Sci. Technol.

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The study of different objects such as: properties of algebraic structures, analysis of chemical graph structures without experiment or understanding networks through topological indices (TIs) is among modern directions in graph theory. The analysis of different networks such as benes network, butterﬂy network, Hex-derived network and biswapped network by using TIs is one of the modern research ﬁelds. The storage and transferring of the data carrying certain information has always remained a modern world problem. The optoelectronic technology used in optical transpose interconnection systems (OTIS) is efﬁcient in outcome over an electrical system due to minimum power consumption and broad bandwidth. By combining the use of wireless and electrical technologies, OTIS has developed into a valuable network and boosted the efﬁciency of contemporary optoelectronic computers. A special type of OTIS is based on the biswapped network over path graph Pn, denoted by B(Pn). In this research work, a maximal twin-preserving subgraph of a biswapped network over path graph Pn is constructed. Moreover, the biswapped network B(Pn) and its constructed subgraph are explored through ev-degree and the ve-degree dependent TIs. A comparative analysis of the ev-degree and the ve-degree dependent TIs for B(Pn) and MT (B(Pn)) (a twin-preserving spanning subgraph of B(Pn)) is among the principal ﬁndings of present work. The analytical formulae, table and the graphical trends are used to describe a comparison between the TIs of the B(Pn) and its maximal twin-preserving subgraph. It is shown that the values of TIs only differ by a constant and does not depend on the value of n. Besides this, to analyse the complexity of MT (B(Pn)) through information functional based entropies, we deﬁne ve-degree and ev-degree based information functionals and compute formulae for ve-degree and ev-degree based entropies using information functionals. Numeric tables and graphs are also used to study complexity of MT (B(Pn)).

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“…To achieve a forecast of a certain property of molecules, topological indices are primarily used; for more information, see [21][22][23]. Finding the extremal graphs on a collection of graphs that satisfy the limitations imposed by the parameters that minimise (or maximise) the value of a topological index, is hence a straightforward challenge [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

On the Hyper Zagreb Index of Trees with a Specified Degree of Vertices

et al. 2023

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Topological indices are the numerical descriptors that correspond to some certain physicochemical properties of a chemical compound such as the boiling point, acentric factor, enthalpy of vaporisation, heat of fusion, etc. Among these topological indices, the Hyper Zagreb index, is the most effectively used topological index to predict the acentric factor of some octane isomers. In the current work, we investigate the extremal values of the Hyper Zagreb index for some classes of trees.

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Conjugated tricyclic graphs with maximum variable sum exdeg index

Cited by 8 publications

References 23 publications

Ad-Hoc Lanzhou Index

Ad-Hoc Lanzhou Index

A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

On the Hyper Zagreb Index of Trees with a Specified Degree of Vertices

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