8.3 Practice Question

Duration: 3 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 demonstrates the application of the Handshaking Lemma in graph theory to solve for an unknown number of vertices. The problem presented involves a simple graph G with 21 edges, where three vertices have a degree of 4 and all remaining vertices have a degree of 2. The instructor systematically applies the fundamental theorem stating that the sum of vertex degrees equals twice the number of edges. By defining the total number of vertices as x, the remaining vertices are expressed as (x-3). The solution process involves setting up a linear equation based on the degree sum, substituting known values, and performing algebraic simplification to isolate x. The final calculation reveals that the graph contains exactly 18 vertices.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with the instructor presenting a graph theory problem displayed on screen: 'A simple graph G contains 21 edges, 3 vertices of degree 4 and all the remaining vertices are of degree 2.' The instructor writes down the Handshaking Lemma formula, explicitly stating that the sum of degrees from i=1 to n equals deg(vi). Key teaching cues include identifying the given values of 21 edges and distinguishing between vertices of degree 4 versus those of degree 2. The instructor underlines key terms in the question to emphasize constraints and sets up the foundational equation required for solving the unknown variable representing total vertices.

  2. 2:00 – 2:41 02:00-02:41

    In the final segment, the instructor executes the algebraic solution derived from the Handshaking Lemma. The visible equation on screen shows 3x4 + (x-3)x2 = 21x2, representing the sum of degrees equating to twice the edge count. The instructor simplifies this expression step-by-step, showing 12 + 2x - 6 = 42. Through algebraic manipulation, the variable x is isolated to find its value. The instructor circles the final answer of 18, confirming that the graph contains 18 vertices total. This section concludes the problem-solving demonstration by verifying the calculation and presenting the definitive result.

The core educational value of this video lies in demonstrating the practical application of the Handshaking Lemma, a fundamental concept in graph theory. The problem serves as a concrete example of how abstract mathematical theorems translate into solvable algebraic equations. By breaking down the problem into identifying knowns (edges and specific vertex degrees) and unknowns (total vertices), the instructor models a systematic approach to graph problems. The transition from theoretical formula to numerical solution highlights the importance of algebraic skills in discrete mathematics. Students should note that defining variables clearly, such as letting x represent total vertices and (x-3) represent remaining vertices, is crucial for setting up correct equations. The final answer of 18 validates the method and reinforces the relationship between edge counts and vertex degrees.

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