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.

The lecture addresses a graph theory problem asking for the count of simple non-isomorphic graphs with 5 vertices and 3 edges. The instructor systematically enumerates possible configurations by drawing labeled vertex sets (a, b, c, d, e) and constructing distinct edge arrangements. Four unique structures are identified: a path graph of length 3, a triangle (cycle C3) with isolated vertices, a star graph K1,3, and a disjoint union of an edge and a path. The visual progression demonstrates how to distinguish non-isomorphic cases based on connectivity and component structure.

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 5 vertices and 3 edges?'. He begins by labeling five points (a, b, c, d, e) on the screen to represent vertices. The visual progression shows him setting up multiple sets of these labeled points, indicating he is preparing to draw different graph configurations systematically. He then draws four distinct diagrams: Graph 1 shows a path of length 3 with an isolated vertex; Graph 2 shows a triangle (cycle C3) with two isolated vertices; Graph 3 shows a central vertex connected to three others (star graph K1,3) with one isolated vertex; Graph 4 shows a path of length 2 and a separate edge. These drawings illustrate the variety of possible structures satisfying the vertex and edge constraints.

  2. 2:00 – 2:06 02:00-02:06

    The final frames display the completed set of four labeled graphs (1, 2, 3, 4) alongside the problem statement. The whiteboard shows 'SANCHIT JAIN SIR' as a watermark, confirming the instructor's identity. The visual evidence concludes the enumeration phase of the problem, presenting the four distinct non-isomorphic configurations derived from systematic construction using labeled vertices a through e.

This session focuses on combinatorial enumeration in graph theory, specifically identifying non-isomorphic simple graphs under fixed vertex and edge counts. The instructor employs a constructive method, starting with labeled vertices to ensure clarity in distinguishing structural differences. Key concepts include isomorphism (structural equivalence), simple graphs (no loops or multiple edges), and connectivity components. The four solutions represent all possible partitions of 3 edges among 5 vertices without creating isomorphic duplicates. The path graph (P4) and disjoint union (P3 + K2) highlight how edge distribution affects component count. The triangle (C3) and star graph (K1,3) demonstrate how cycles and centralization create unique topologies. This systematic approach ensures no valid configuration is missed while avoiding overcounting due to symmetry.

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