Related Experiment Video
Updated: Oct 2, 2025
09:32
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
Published on: December 18, 2016
12.6K
Power Graphs of Finite Groups Determined by Hosoya Properties
Fawad Ali1, Bilal Ahmad Rather2, Anwarud Din3
1Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Pakistan.
Entropy (Basel, Switzerland)
|February 25, 2022
Summary
This study explores Hosoya characteristics of power graphs in molecular symmetries. We determined the Hosoya index for dihedral and generalized groups, useful for chemical descriptors.
Area of Science:
- Graph theory
- Combinatorial chemistry
- Algebraic structures
Background:
- The power graph P(G) connects elements where one is a power of another.
- Hosoya polynomials and their reciprocals reveal graph invariants related to distance.
- Topological indices like the Z-index (Hosoya index) are crucial in combinatorial chemistry.
Purpose of the Study:
- To investigate the Hosoya characteristics (polynomial and reciprocal) of power graphs associated with molecular symmetries.
- To determine the Hosoya index for power graphs of dihedral and generalized groups.
Main Methods:
- Utilized graph theory definitions for power graphs.
- Applied concepts of Hosoya polynomials and their properties.
- Calculated the Hosoya index for specific algebraic structures.
Main Results:
- The Hosoya characteristics of power graphs for symmetries of regular molecular gones were analyzed.
- The Hosoya index was successfully determined for the power graphs of dihedral and generalized groups.
Conclusions:
- The findings provide valuable data for calculating distance-dependent chemical descriptors.
- This research bridges graph theory and chemistry by applying graph invariants to molecular structures.
Related Concept Videos
01:08Hückel's Rule Diagram of π MOs: Frost Circle
4.9K
The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...
4.9K
01:10Vector Algebra: Graphical Method
15.0K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
15.0K
01:12Bewley Lattice Diagram
911
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
911
01:07Ogive Graph
6.0K
An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this...
6.0K
01:18pV-Diagrams
4.6K
The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
4.6K
01:15Dimensionless Groups in Fluid Mechanics
505
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
505