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Graph Theory

Graph theory mathematics ki woh branch hai jo graphs ka study karti hai — vertices (points) aur…

Overview

Graph Theory — Quick Facts

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Property: Detail

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Full Name: Graph Theory

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Field: Discrete Mathematics /…

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Founder: Leonhard Euler (1736)

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Infobox

📚 | Property | Detail | |---|---| | Full Name | Graph Theory | | Field | Discrete…

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Itihaas — Königsberg Bridge Problem

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Har land mass ko ek vertex maano,…

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Walk me har vertex pe "enter +…

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Lekin Königsberg me sab vertices…

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Isliye aisi walk (Eulerian path)…

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Fundamental Concepts

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Graph: G = (V, E) — vertices ka…

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Vertex (Node): Graph ka…

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Edge (Link): Do vertices ka…

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Degree: Vertex se connected edges…

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Types of Graphs

⭐ | Type | Description | Example | |---|---|---| | Undirected | Edges ka direction nahi |…

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Graph Properties aur Measures

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Connected graph: Har pair ke beech…

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k-connected: Graph connected rehta…

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Bridge: Edge jise remove karne se…

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Cut vertex (Articulation point):…

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Famous Problems in Graph Theory

✨ | Problem | Description | Status | Significance | |---|---|---|---| | Königsberg Bridges…

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Important Theorems

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Eulerian circuit (sab edges…

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Eulerian path exist karta hai iff:…

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Sab vertices ki degrees ka sum = 2…

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$\sum_{v \in V} \deg(v) = 2|E|$

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Graph Theory in Computer Science

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Graph data structure (adjacency…

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Tree — special case of graph…

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Heap — tree-based, which is…

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Trie — tree structure for string…

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Branches of Graph Theory

📚 | Branch | Focus | Application | |---|---|---| | Algebraic Graph Theory | Graph…

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Real-World Applications

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Social Networks — Friend…

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Transportation — Route planning…

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Internet — Web page ranking…

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Biology — Protein interaction…

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Notable Mathematicians

🎯 | Mathematician | Contribution | Year | |---|---|---| | Leonhard Euler | Founded graph…

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Limitations aur Open Problems

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NP-hard problems — Bahut se graph…

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Large-scale graphs — Billions of…

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Dynamic graphs — Time-varying…

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Hypergraphs — Standard graph…

Diagram

Visual Flow

📊 Diagram visualization — details in narration

Quiz — Question 1

Graph Theory ka sabse sahi definition kya hai?

Quick Quiz

Quiz — Question 2

Graph Theory ka 'Full Name' kya hai?

Complete! 🎉

Graph Theory Complete!

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Graph Theory Complete

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