Practice Question

Duration: 4 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 addresses a graph theory problem: determining the number of simple non-isomorphic graphs possible with three vertices. The instructor begins by introducing the question on screen, asking for the count of unique graph structures where vertices are labeled 'a', 'b', and 'c'. The core concept involves distinguishing between isomorphic graphs, which share the same structure despite different vertex labels or positions, and non-isomorphic graphs, which represent fundamentally distinct connectivity patterns. The instructor employs a systematic enumeration method, drawing all possible edge configurations for the three vertices to visualize every potential graph. This includes cases with zero edges, single edges, pairs of edges forming paths or branches, and the complete graph (triangle) with three edges. By visually comparing these configurations, the instructor identifies duplicates that are structurally identical and crosses them out to ensure only unique structures remain. The process culminates in a final count of four distinct non-isomorphic graphs, which is circled as the solution.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement displayed on screen: 'Q How many simple non isomorphic graphs are possible with 3 vertices?'. He sets up the visual foundation by drawing three distinct points labeled 'a', 'b', and 'c' to represent the vertices. The teaching flow moves from defining the problem parameters to establishing a systematic approach for enumeration. Key visible events include the instructor drawing graphs with varying edge counts, starting from an empty set of edges and progressing to single connections. The instructor demonstrates the concept of non-isomorphism by showing how different edge configurations create unique structures, such as a path versus a disconnected set. This initial phase establishes the methodology of visualizing all possible combinations before filtering for uniqueness.

  2. 2:00 – 3:30 02:00-03:30

    The instructor continues the enumeration process by drawing additional graph configurations and labeling them sequentially from 1 to 8. He actively analyzes each drawn structure to check for isomorphism against previously identified graphs. The visual evidence shows the instructor crossing out specific graph examples that are structurally identical to earlier ones, effectively eliminating duplicates from the count. This elimination process is crucial for ensuring that only non-isomorphic graphs are included in the final tally. The segment concludes with the instructor circling the number 4, indicating that there are exactly four simple non-isomorphic graphs possible with three vertices. The final board displays the circled answer alongside the various graph sketches that led to this conclusion, providing a clear visual summary of the solution.

The video effectively demonstrates a combinatorial approach to graph theory by using visual enumeration. The instructor's method relies on drawing all possible edge combinations for a fixed number of vertices and then applying the definition of isomorphism to filter out redundant structures. The key takeaway is that for three vertices, there are exactly four unique connectivity patterns: the empty graph (0 edges), a single edge with one isolated vertex (1 edge), two edges forming a path (2 edges), and the complete triangle graph (3 edges). This practical example reinforces the theoretical definition of non-isomorphism by showing how structural equivalence is determined visually. The step-by-step elimination process highlights the importance of careful comparison in combinatorial problems.

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