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19 pages, 308 KB

Open AccessFeature PaperEditor’s ChoiceArticle

On the Exponential Atom-Bond Connectivity Index of Graphs

by Kinkar Chandra Das

Mathematics 2025, 13(2), 269; https://doi.org/10.3390/math13020269 - 15 Jan 2025

Cited by 7 | Viewed by 3185

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological [...] Read more.

e^{ABC} = e^{ABC} (Υ) = \sum_{v_{i} v_{j} \in E (Υ)} e^{\sqrt{\frac{d_{i} + d_{j} - 2}{d_{i} d_{j}}}},

where

d_{i}

is the degree of the vertex

v_{i}

Υ

. In this paper, we prove that the double star

D S_{n - 3, 1}

is the second maximal graph with respect to the

e^{ABC}

index of trees of order n. We give an upper bound on

e^{ABC}

of unicyclic graphs of order n and characterize the maximal graphs. The graph

K_{1} \lor (P_{3} \cup (n - 4) K_{1})

gives the maximal graph with respect to the

e^{ABC}

index of bicyclic graphs of order n. We present several relations between

e^{ABC} (Υ)

and

A B C (Υ)

of graph

Υ

. Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research. Full article

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11 pages, 3129 KB

Open AccessArticle

On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q]

by Young Chel Kwun, Abaid Ur Rehman Virk, Waqas Nazeer, M. A. Rehman and Shin Min Kang

Symmetry 2018, 10(8), 320; https://doi.org/10.3390/sym10080320 - 3 Aug 2018

Cited by 38 | Viewed by 5717

Abstract

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon

S i_{2} C_{3^{-}} I [p, q]

and

S i_{2} C_{3^{-}} II [p, q]

second. Full article

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21 pages, 4138 KB

Open AccessArticle

On Topological Properties of Symmetric Chemical Structures

by Muhammad Imran, Muhammad Kamran Siddiqui, Muhammad Naeem and Muhammad Azhar Iqbal

Symmetry 2018, 10(5), 173; https://doi.org/10.3390/sym10050173 - 18 May 2018

Cited by 64 | Viewed by 5234

Abstract

The utilizations of graph theory in chemistry and in the study of molecule structures are more than someone’s expectations, and, lately, it has increased exponentially. In molecular graphs, atoms are denoted by vertices and bonds by edges. In this paper, we focus on [...] Read more.

S i_{2} C_{3}

-I and

S i_{2} C_{3}

I I

. Moreover, we have computed topological indices, namely general Randić Zagreb types indices, geometric arithmetic index, atom–bond connectivity index, fourth atom–bond connectivity and fifth geometric arithmetic index of

S i_{2} C_{3}

-I and

S i_{2} C_{3}

I I

. Full article

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Figure 1

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