Related Experiment Video
Updated: Jul 19, 2025
05:30
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
Published on: September 8, 2023
604
Computing The Energy of Certain Graphs based on Vertex Status.
Asim Khurshid1, Muhammad Salman1
1Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan.
Current Organic Synthesis
|August 15, 2023
Summary
This study introduces a new method to calculate graph energy using vertex status, extending Hückel molecular orbital theory. The research explores graph energy for various graph families, offering numerical and graphical comparisons.
Area of Science:
- Graph theory
- Mathematical chemistry
- Quantum chemistry
Background:
- Hückel molecular orbital theory provides a framework for computing graph energy.
- Vertex status is a key factor in determining graph energy.
- Existing methods for graph energy calculation can be enhanced.
Purpose of the Study:
- To explore graph energy using a novel approach based on vertex status.
- To investigate the status adjacency matrix and its Laplacian version.
- To analyze graph energy for diverse graph families.
Main Methods:
- Eigenvalue computation of adjacency and Laplacian matrices.
- Matrices are constructed based on vertex status.
- Numerical and graphical analysis of results.
Main Results:
- Exact status sum and Laplacian status sum energies were determined for complete graphs, complete bipartite graphs, star graphs, bistar graphs, barbell graphs, and thorny graphs.
- Numerical and graphical comparisons of calculated energies were performed.
Conclusions:
- Introduced the status sum adjacency matrix and its Laplacian version.
- Extended the study of graph spectrum and energy.
- Visualized and investigated these new concepts for various graph types.
Related Concept Videos
01:14Energy Diagrams - I
5.0K
The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...
5.0K
01:10Energy Diagrams - II
4.7K
Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...
4.7K
01:12Power and Energy
898
The power and energy delivered to an element are subjects of great significance in the field of electrical engineering. It is a well-known fact that a 100-watt light bulb emits more light than a 60-watt one. Therefore, power and energy calculations play a crucial role in the analysis of electrical circuits.
Power, defined as the time rate of expending or absorbing energy, is quantified in units called watts (W). The relation between power and energy is mathematically given as
Power, defined as the time rate of expending or absorbing energy, is quantified in units called watts (W). The relation between power and energy is mathematically given as
898
01:21Energy Associated With a Charge Distribution
1.6K
The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
1.6K
01:17Energy and Power Signals
338
In an electrical system with a resistor, voltage and current signals facilitate the measurement of power and energy across the resistor. For a continuous-time signal, the total energy over a time interval is defined as the integral of the square of the signal's magnitude over that interval. Mathematically, this is expressed as:
338
01:10Vector Algebra: Graphical Method
12.2K
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...
12.2K