Bi-Partie Graph

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/UP-LT-GRADE-ASSISTANT-TEACHER-2025/digital-logic-circuits-discrete-math-structures/graph-theory/bipartite-cycle-regular-and-complement-of-a-graph/asset-bi-partie-graph after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography: Geography
  16. GS Paper | 02 | History: History
  17. GS Paper | 03 | Indian Economy & Social Development: Indian Economy
  18. GS Paper | 04 | General Science: Biology, Chemistry, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research
  19. GS Paper | 05 | Elementary Maths: संख्या पद्धति / Number System, Divisibility Rules, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, प्रतिशत / Percentage, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, समय और कार्य / Time and Work, समय, चाल और दूरी / Time, Speed and Distance, Algebra, घन क्षेत्रमिति / Solid Mensuration, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, Statistics, Probability, Sequence and Series (Series), मिश्रण और एलिगेशन / Mixture and Alligation, Calculus, Trigonometry, Vectors, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, यूक्लिडीय ज्यामिति और क्षेत्रमिति / Euclidean Geometry and Mensuration, सांख्यिकी और प्रायिकता / Statistics and Probability, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers, समतल क्षेत्रमिति / Plane Mensuration, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics
  20. GS Paper | 06 | Indian Polity and Governance: Polity
  21. GS Paper | 07 | Current Events: समसामयिकी / Current Affairs
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture covers the definitions and properties of Bi-partite and Complete Bi-partite graphs. The instructor defines a Bi-partite graph as one where vertices are partitioned into two disjoint sets such that edges only connect vertices from different sets. He then defines a Complete Bi-partite graph where every vertex in one set connects to every vertex in the other, denoted as $K_{m,n}$. The lecture includes visual demonstrations and formula derivations for edge counts.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by defining a **Bi-partite graph**. He reads the formal definition from the slide: "A graph G(V, E) is called bi-partite graph if it's vertex set V(G) can be partitioned into two non-empty disjoint subset V1(G) and V2(G) in such a way that each edge e in E(G) has it's one end point in V1(g) and other end point in V2(g)." He emphasizes the condition that edges must connect vertices from different sets, not within the same set. He underlines key terms like "partitioned", "non-empty disjoint subset", and "one end point". He then illustrates this with a diagram, circling the left column of red vertices as set V1 and the right column of black vertices as set V2. He explains that the partition $V = V1 \cup V2$ is called the bipartition of G. He then introduces the second concept, **Complete Bi-partite graph**, reading the definition: "A Bi-partite graph G(V, E) is called Complete bi-partite graph if every vertex in the first partition is connected to every vertex in the second partition, denoted by $K_{m,n}$."

  2. 2:00 – 3:46 02:00-03:46

    The instructor elaborates on the **Complete Bi-partite graph** notation $K_{m,n}$. He writes $|V1| = m$ and $|V2| = n$ to represent the size of the two partitions. He explains that in a complete bipartite graph, the total number of edges is the product of the sizes of the two sets, writing $K_{m,n} = m imes n$. He draws a square graph with vertices labeled 1, 2, 3, 4 to demonstrate a bipartite structure, circling vertices 1 and 3 as one set and 2 and 4 as the other. He then draws a specific example of a complete bipartite graph with 3 vertices on the left and 3 on the right, labeling it $K_{3,3}$. He draws lines connecting every left vertex to every right vertex to show the "complete" nature. He also draws a graph with 4 vertices (1, 2, 3, 4) in a cycle, circling 1 and 3, and 2 and 4 to show it is bipartite. He emphasizes that for a graph to be bipartite, you must be able to divide vertices into two sets such that no two vertices within the same set are connected.

The lecture systematically builds the concept of bipartite graphs. It starts with the fundamental definition involving vertex partitioning and edge constraints. It then moves to the specific case of complete bipartite graphs, where connectivity is maximized between the two sets. The instructor uses visual aids, underlining text, and hand-drawn diagrams to reinforce the definitions. Key takeaways include the notation $K_{m,n}$, the condition for bipartition, and the formula for the number of edges in a complete bipartite graph ($m imes n$).

Loading lesson…