Practice Question

Duration: 2 min

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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
  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.

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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