Practice Question

Duration: 2 min

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Module outline

  1. Discrete Mathematics: Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  2. Digital Logic: Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Pipelining, Multiprocessors
  4. Programming: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
  5. Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  6. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  7. Theory of Computation: Grammar, Regular Language Properties, Moore & Mealy Machines, Turing Machines
  8. 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, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  9. Operating Systems: 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, Security
  10. Database Management Systems: 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, ORDBMS, NoSQL
  11. Computer Networks: 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
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment focuses on a graph theory problem: determining the number of simple non-isomorphic graphs possible with 4 vertices and 3 edges. The instructor begins by establishing the foundational parameters, labeling four distinct points as 'a', 'b', 'c', and 'd' to represent the vertices. This setup is crucial for systematically constructing potential graph configurations without duplication. The core task involves visualizing how these vertices can be connected by exactly three edges while ensuring the resulting graphs are non-isomorphic, meaning they cannot be transformed into one another through relabeling. The instructor demonstrates this by drawing three specific distinct structures: a path graph (P4), a star graph (K1,3), and a triangle with an isolated vertex. The visual progression moves from setting up the labeled vertices to sketching these unique topological arrangements, highlighting connectivity and cycle properties as key differentiators for isomorphism.

Chapters

  1. 0:00 – 1:59 00:00-01:59

    The instructor introduces the problem 'How many simple non isomorphic graphs are possible with 4 vertices and 3 edges?' visible on screen. He labels four points 'a', 'b', 'c', and 'd' to serve as vertices. He then systematically draws three distinct configurations: a path graph, a star graph (K1,3), and a triangle with an isolated vertex. The instructor circles the number '2' or writes '3' to indicate the count of non-isomorphic graphs found, demonstrating visual enumeration techniques for graph theory.

The video provides a concise, practical demonstration of enumerating non-isomorphic graphs using visual construction. By fixing four vertices and varying edge connections, the instructor illustrates that topology determines isomorphism rather than vertex labels. The three primary structures identified—a linear path, a central hub star, and a cycle with an outlier—exhaust the possibilities for this specific constraint. This method emphasizes that non-isomorphism requires distinct structural properties, such as degree sequences or connectivity patterns. The circled numbers suggest a verification step where the instructor confirms the final count of valid configurations.

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