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https://github.com/abhinav-reddy-k/daa
https://github.com/abhinav-reddy-k/daa
Last synced: 6 days ago
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- Host: GitHub
- URL: https://github.com/abhinav-reddy-k/daa
- Owner: Abhinav-Reddy-k
- Created: 2024-11-01T19:44:52.000Z (3 months ago)
- Default Branch: master
- Last Pushed: 2024-11-01T21:08:13.000Z (3 months ago)
- Last Synced: 2024-11-01T22:18:13.697Z (3 months ago)
- Language: Python
- Size: 347 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Graph Structures Project
This project contains implementations of various graph structures, each with unique characteristics and properties. The
graphs are represented using Python and stored as adjacency lists.
## Graph Structures
### 1. Homogeneous Lobster Graph Plus 1 \( \{Lob}(n, p) \)
The **Lobster Graph** is constructed with a central path graph and two star graphs on each side for alternative nodes.
- **Description**:
- A central path graph \( P_n \) with \( n \) vertices.
- Two star graphs \( S_p \), each containing \( p \) vertices.
- The central vertex of each star graph connects to every vertex of the path graph.
- **Total Vertices**:
\[
n(2p + 1) / 2
\]
- **Vertex k-labeling**: The Lobster Graph allows for edge irregular k-labeling, ensuring that each edge has a unique
weight.
### 2. Homogeneous Amalgamated Star \( S(n, m) \)
The **Homogeneous Amalgamated Star** graph consists of a central node connected to \( n \) outward vertices, with each
outward vertex connecting to \( m \) vertices.
- **Description**:
- A central node that connects to \( n \) vertices.
- Each of the \( n \) vertices is connected to \( m-1 \) additional vertices, forming a star-like structure.
- **Total Vertices**:
\[
m \times n + 1
\]
- **Edge Irregular k-labeling**: This graph supports edge irregular labeling, ensuring all edge weights are distinct.
### 3. Amalgamated Triangle Star
The **Amalgamated Triangle Star** graph consists of a central node with \( n \) outward vertices, each forming a
triangle with two additional vertices.
- **Description**:
- A central node connects to \( n \) outward vertices.
- Each outward vertex forms a triangle with two additional vertices, creating a closed loop.
- **Graph Structure**:
- Central Vertex: `C`
- Outward Vertices: `O_i` (connected to `C`)
- Triangle Vertices: `T_{i1}`, `T_{i2}` for each `O_i`
### 4. Cyclic Star with Branches
The **Cyclic Star with Branches** graph features a central vertex connected to \( n \) vertices arranged in a circular
manner, with each of these vertices having two outer vertices.
- **Description**:
- A central vertex connects to \( n \) vertices.
- Each vertex is connected in a circular formation (cycle).
- Each vertex also has two outer vertices connected to it, which are not connected to each other.
- **Graph Structure**:
- Central Vertex: `C`
- Vertices: `V_i` (connected to `C` and each other)
- Outer Vertices: `O_{ij}` for each `V_i`
## Installation
To run the code, you will need Python installed on your machine. Clone this repository and run the individual graph
construction functions provided in each graph section.
```bash
git clone https://github.com/Abhinav-Reddy-k/DAA.git
cd DAA
```
To install the required Python packages, use the following steps:
1. Ensure you have Python and `pip` installed. You can check this by running:
```bash
python --version
pip --version
```
2. Install the required packages using the following command:
3. ```bash
pip install -r requirements.txt
```
Go to each file of a particular graph, adjust the parameters and just run the code.
## Images
### 1. Homogeneous Lobster Graph Plus 1
### 2. Homogeneous Amalgamated Star
### 3. Star of Triangles
### 4. Cyclic Star with Branches
