{"id":25059864,"url":"https://github.com/abhinav-reddy-k/daa","last_synced_at":"2025-03-31T11:14:57.014Z","repository":{"id":260693179,"uuid":"882059780","full_name":"Abhinav-Reddy-k/DAA","owner":"Abhinav-Reddy-k","description":null,"archived":false,"fork":false,"pushed_at":"2024-11-07T18:17:27.000Z","size":356,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-02-06T16:05:43.636Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Abhinav-Reddy-k.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2024-11-01T19:44:52.000Z","updated_at":"2024-11-07T18:17:31.000Z","dependencies_parsed_at":"2024-11-01T22:18:17.625Z","dependency_job_id":"8302ad3d-a214-4036-897e-4c25fbae7f03","html_url":"https://github.com/Abhinav-Reddy-k/DAA","commit_stats":null,"previous_names":["abhinav-reddy-k/daa"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Abhinav-Reddy-k%2FDAA","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Abhinav-Reddy-k%2FDAA/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Abhinav-Reddy-k%2FDAA/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Abhinav-Reddy-k%2FDAA/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Abhinav-Reddy-k","download_url":"https://codeload.github.com/Abhinav-Reddy-k/DAA/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":246458009,"owners_count":20780678,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2025-02-06T15:55:25.724Z","updated_at":"2025-03-31T11:14:56.982Z","avatar_url":"https://github.com/Abhinav-Reddy-k.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Graph Structures Project\n\nThis project contains implementations of various graph structures, each with unique characteristics and properties. The\ngraphs are represented using Python and stored as adjacency lists.\n\n## Graph Structures\n\n### 1. Homogeneous Lobster Graph Plus 1 \\( \\{Lob}(n, p) \\)\n\nThe **Lobster Graph** is constructed with a central path graph and two star graphs on each side for alternative nodes.\n\n- **Description**:\n    - A central path graph \\( P_n \\) with \\( n \\) vertices.\n    - Two star graphs \\( S_p \\), each containing \\( p \\) vertices.\n    - The central vertex of each star graph connects to every vertex of the path graph.\n\n- **Total Vertices**:\n  \\[\n  n(2p + 1) / 2\n  \\]\n\n- **Vertex k-labeling**: The Lobster Graph allows for edge irregular k-labeling, ensuring that each edge has a unique\n  weight.\n\n### 2. Homogeneous Amalgamated Star \\( S(n, m) \\)\n\nThe **Homogeneous Amalgamated Star** graph consists of a central node connected to \\( n \\) outward vertices, with each\noutward vertex connecting to \\( m \\) vertices.\n\n- **Description**:\n    - A central node that connects to \\( n \\) vertices.\n    - Each of the \\( n \\) vertices is connected to \\( m-1 \\) additional vertices, forming a star-like structure.\n\n- **Total Vertices**:\n  \\[\n  m \\times n + 1\n  \\]\n\n- **Edge Irregular k-labeling**: This graph supports edge irregular labeling, ensuring all edge weights are distinct.\n\n### 3. Amalgamated Triangle Star\n\nThe **Amalgamated Triangle Star** graph consists of a central node with \\( n \\) outward vertices, each forming a\ntriangle with two additional vertices.\n\n- **Description**:\n    - A central node connects to \\( n \\) outward vertices.\n    - Each outward vertex forms a triangle with two additional vertices, creating a closed loop.\n\n- **Graph Structure**:\n    - Central Vertex: `C`\n    - Outward Vertices: `O_i` (connected to `C`)\n    - Triangle Vertices: `T_{i1}`, `T_{i2}` for each `O_i`\n\n### 4. Cyclic Star with Branches\n\nThe **Cyclic Star with Branches** graph features a central vertex connected to \\( n \\) vertices arranged in a circular\nmanner, with each of these vertices having two outer vertices.\n\n- **Description**:\n    - A central vertex connects to \\( n \\) vertices.\n    - Each vertex is connected in a circular formation (cycle).\n    - Each vertex also has two outer vertices connected to it, which are not connected to each other.\n\n- **Graph Structure**:\n    - Central Vertex: `C`\n    - Vertices: `V_i` (connected to `C` and each other)\n    - Outer Vertices: `O_{ij}` for each `V_i`\n\n## Installation\n\nTo run the code, you will need Python installed on your machine. Clone this repository and run the individual graph\nconstruction functions provided in each graph section.\n\n```bash\ngit clone https://github.com/Abhinav-Reddy-k/DAA.git\ncd DAA\n```\n\nTo install the required Python packages, use the following steps:\n\n1. Ensure you have Python and `pip` installed. You can check this by running:\n   ```bash\n   python --version\n   pip --version\n    ```\n2. Install the required packages using the following command:\n3. ```bash\n   pip install -r requirements.txt\n   ```\n\nGo to each file of a particular graph, adjust the parameters and just run the code.\n\n## Images\n\n### 1. Homogeneous Lobster Graph Plus 1\n\n![homogeneous_lobster_+1.png](images/homogeneous_lobster_+1.png)\n\n### 2. Homogeneous Amalgamated Star\n\n![amalgamated_star.png](images/amalgamated_star.png)\n\n### 3. Star of Triangles\n\n![star_of_triangles.png](images/star_of_triangles.png)\n\n### 4. Cyclic Star with Branches\n\n![cyclic_star_with_branches.png](images/cyclic_star_with_branches.png)","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fabhinav-reddy-k%2Fdaa","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fabhinav-reddy-k%2Fdaa","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fabhinav-reddy-k%2Fdaa/lists"}