9.2 Practice Question

Duration: 2 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  3. Paper-2 | Databases / DBMS & SQL: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: 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, Network Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. Paper-2 | Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. Paper-2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment focuses on solving graph theory practice problems using the Handshaking Lemma. The instructor demonstrates how to determine vertex constraints based on edge counts and degree limits. Key concepts include the relationship where the sum of all vertex degrees equals twice the number of edges (2|E|). The session covers two primary problem types: finding maximum vertices given a minimum degree constraint and finding minimum vertices given a maximum degree constraint. The instructor applies inequalities to bound the number of vertices, ensuring results are rounded appropriately for integer solutions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by addressing a problem asking for the maximum number of vertices in a simple graph with 35 edges where each vertex has a degree of at least 3. The on-screen text displays the question: 'Q Maximum no of vertex in a simple graph with 35 edges and degree of each vertex is at least 3 is ____?'. The instructor applies the Handshaking Lemma, calculating the sum of degrees as 35 * 2 = 70. To find the upper bound for vertices, they divide this sum by the minimum degree (3), resulting in 70/3. The calculation is shown as '20 / 3' on screen, which the instructor rounds down to find the maximum possible integer vertices. The final answer is circled as 23, though the arithmetic shown suggests a discrepancy or specific rounding logic used in class.

  2. 2:00 – 2:25 02:00-02:25

    The video transitions to a second problem asking for the minimum number of vertices possible in a simple graph with 41 edges where each vertex has a degree of at most 5. The text on screen reads: 'Q Minimum number of vertices possible in a simple graph if 41 edges and degree of each vertex is at most 5?'. The instructor calculates the total degree sum as 41 * 2 = 82. They set up an inequality where the maximum degree (5) times the number of vertices (|V|) must be at least 82, written as '5 x |V| >= 82'. Solving for |V| gives approximately 16.4, which is displayed as '< 16.4'. Since vertices must be whole numbers, the instructor rounds up to conclude the minimum number of vertices is 17.

The lecture effectively demonstrates the practical application of the Handshaking Lemma for bounding graph parameters. The instructor consistently uses the formula sum(degrees) = 2 * edges to establish a total degree budget. For maximum vertex counts, the strategy involves dividing this budget by the minimum allowed degree per vertex and rounding down. Conversely, for minimum vertex counts, the instructor divides the budget by the maximum allowed degree and rounds up. This approach ensures that the resulting integer vertex count satisfies the given edge and degree constraints simultaneously.

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