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 1 | General Studies: State Wise GK / राज्यवार सामान्य ज्ञान (GK)
  3. Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
  4. Paper 1 | Current Affairs: GK- Current Affairs / GK- समसामयिकी
  5. Paper 2 | Discrete Mathematical Structure: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता
  6. Paper 2 | Digital Computer Organization And Architecture: Number System, Number Representation, Sequential Circuits, Combinational Circuit, 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. Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  8. Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References, Generic & Collections
  9. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  10. Paper 2 | Data Structure And Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Advanced Algorithms
  11. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS
  12. 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, Complexity Theory
  13. 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
  14. Paper 2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Enhanced Data Models
  15. Paper 2 | Computer Network And Information Security: Introduction to CN, Data Communication, Application Layer, Hardware basics, Cyber Threats and Malware Attacks, Network Security, 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
  16. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Current Trends & Technologies: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms, Data Warehousing & Mining, Electronic Data Interchange and E-Commerce
  18. Paper 2 | Full Length Mock Tests:
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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