Further development of F-index for fuzzy graph and its application in Indian railway crime

Topological characterization of 3D molecular structures is an emerging study area in theoretical and computational chemistry. These structural descriptors are used in a variety of domains, including chemical graph theory, drug delivery, and nanomaterial characterization. Quantitative structural descriptors can be used to characterize the chemical and physical properties of a given compound. Topological indices of molecular graphs are numerical quantities that allow us to collect information about the chemical structure and reveal its hidden qualities without performing experiments. Due to the low cost of implementation, zeolite networks are considered popular chemical networks. Zeolites are widely used networks with applications in chemistry, medicine, and commercial production owing to their excellent chemical features. The sodalite network is composed of a very unique type of zeolite framework called sodalite. It is a three-dimensional network of interconnected cages and tunnels that provide an ideal environment for a wide range of chemical and physical processes. This paper deals with the sodalite material network’s degree-based and reverse degree-based irregularity indices. These indices provide a quantitative measure of the irregular behaviour of the sodalite material network. It can be used to identify areas of the network where irregular behaviour is occurring and to compare different networks to determine which is more irregular. Additionally, these indices can be used to monitor changes in irregularity over time, allowing us to measure the impact of any interventions that are implemented.

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Structural Modelling and Characterization of Sodalite Material Network concerning the Irregularity Topological Indices

Zaman¹,

Salman²,

Ullah

et al. 2023

“…In [21], authors considered the Zagreb index and investigated for crisp graphs and also for fuzzy graphs which is a very important tool in network, molecular chemistry, and many other felds. In [22], authors considered the F-index for fuzzy graphs and applications in railway crime. For various other applications and nation, we refer [8,9,[23][24][25][26][27] to the readers.…”

Section: Introductionmentioning

confidence: 99%

Sharp Bounds of Kulli–Basava Indices in Generalized Form for k-Generalized Quasi Trees

Afridi

Khan

Ali

et al. 2023

Molecular descriptors are a basic tool in the spectral graph, molecular chemistry, and various other fields of mathematics and chemistry. Kulli–Basava K B indices were initiated for chemical applications of various substances in chemistry. For simple graph G , K B indices in generalized forms are K B 1 ϱ G = ∑ g h ∈ E G S e g + S e h ϱ and K B 2 ϱ G = ∑ g h ∈ E G S e g . S e h ϱ , where S e g = ∑ e ∈ N e g d G e , and for edge e = g , h , the degree is d G e = d G g + d G h − 2 and ϱ ≠ 0 is any real number. The graph G is said to be a k − g e n e r a l i z e d quasi tree if for the vertex set U k ⊂ G having U k = k , G − U k is a tree and for U k − 1 ⊂ V G having U k − 1 = k − 1 , G − U k − 1 is not a tree. In this research work, we have successfully investigated sharp bounds of generalized K B indices for k-generalized quasi trees where ϱ ≥ 1 . Chemical applications of the generalized form are also studied for alkane isomers with scatter diagrams and residuals.

“…Islam and Pal [18] presented the First Zagreb Index for fuzzy graphs and discussed its application too. In [19], a new index, the F-index, has been already investigated and improved. In 2022, Rajeshwari et al [20] established the fuzzy topological indices for bipolar fuzzy graphs.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Topological Characterization of $q C_{n}$ Graph via Fuzzy Topological Indices

Mufti,

Anjum,

Tawfiq

et al. 2023

Fuzzy topological indices are one of the accomplished mathematical approaches for numerous technology, engineering, and real-world problems such as telecommunications, social networking, traffic light controls, marine, neural networks, Internet routing, and wireless sensor network (Muneera et al. (2021)). This manuscript comprises the study of a particular class of graphs known as q C n snake graphs. Some innovative results regarding fuzzy topological indices have been established. The major goal of the work is to introduce the notions of First Fuzzy Zagrab Index, Second Fuzzy Zagrab Index, Randic Fuzzy Zagrab Index, and Harmonic Fuzzy Zagrab Index of the q C n snake graph.