Computing weighted Szeged and PI indices from quotient graphs

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Szeged, PI and Mostar indices are some of the most investigated distance‐based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called Szeged‐like topological indices. In this paper, we formally introduce the concept of a general Szeged‐like topological index, which includes all mentioned indices and also infinitely many other topological indices that can be defined in a similar way. As the main result of the paper, we provide a cut method for computing a general Szeged‐like topological index for any strength‐weighted graph. This greatly generalizes various methods known for some of the mentioned indices and therefore rounds off such investigations. Moreover, we provide applications of our main result to benzenoid systems, phenylenes, and coronoid systems, which are well‐known families of molecular graphs. In particular, closed‐form formulas for some subfamilies of these graphs are deduced.

Section: A General Cut Methodsmentioning

confidence: 99%

Section: Applications To Molecular Graphsmentioning

confidence: 99%

See 1 more Smart Citation

General cut method for computing Szeged‐like topological indices with applications to molecular graphs

Brezovnik

Tratnik

2020

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“…For each i ∈ {1, …, k }, we define the function ℓ i : V ( G ) → V ( G i ) as follows: for any u ∈ V ( G ), let ℓ i ( u ) be the connected component U of the graph G − E i such that u ∈ V ( U ). The following lemma from references will be firstly needed.Lemma If e = uv ∈ E i , where i ∈ {1 , … , k} , then U = ℓ i (u) and V = ℓ i (v) are adjacent vertices in G i , that is , E = UV ∈ E(G i ) . Moreover ,

\begin{matrix} lefttrue \\ N_{u} (e| G) = \underset{X \in N_{U} (E| G_{i})}{\cup} V (X), \\ N_{v} (e| G) = \underset{X \in N_{V} (E| G_{i})}{\cup} V (X), \\ M_{u} (e| G) = (\underset{X \in N_{U} (E| G_{i})}{\cup} E (X)) \cup (\underset{F \in M_{U} (E| G_{i})}{\cup} \overset{false^}{F}), \\ M_{v} (e| G) = (\underset{X \in N_{V} (E| G_{i})}{\cup} E (X)) \cup (\underset{F \in M_{V} (E| G_{i})}{\cup} \overset{false^}{F}) . \end{matrix}

Lemma Let G sw be a strength‐weighted graph.…”

Section: The Main Resultsmentioning

confidence: 99%

Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems

Arockiaraj¹,

Clement

Tratnik

2019

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On the great success of bond‐additive topological indices such as Szeged, Padmakar‐Ivan, Zagreb, and irregularity measures, yet another index, the Mostar index, has been introduced recently as a quantitative refinement of the distance nonbalancedness and also a peripherality measure in molecular graphs and networks. In this direction, we introduce other variants of bond‐additive indices, such as edge‐Mostar and total‐Mostar indices. The present article explores a computational technique for Mostar, edge‐Mostar, and total‐Mostar indices with respect to the strength‐weighted parameters. As an application, these techniques are applied to compute the three indices for the family of coronoid and carbon nanocone structures.

“…Topological indices are important graph invariants used for describing various properties of molecules. Methods for computing topological indices of some molecular graphs such as benzenoid systems, phenylenes or coronoid systems were studied in [25][26][27]. In this section, we study the Sombor indices of graphene, coronoid systems and carbon nanocones.…”

Section: The Sombor Indices Of Graphene Coronoid Systems and Carbon Nanoconesmentioning

confidence: 99%

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Fang

You

Liu

2021

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones.