Practice Question

Duration: 2 min

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Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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 Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, 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, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: 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, Database Recovery, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full 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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