13.1 Practice Question

Duration: 2 min

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Module outline

  1. HPSC Interview Preparation: Interview Preparation
  2. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  3. Data Structure & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Sorting Algorithms, Minimum Spanning Trees, Time Complexity Analysis, Graph Theory, Shortest Path Algos
  4. Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  5. Computer System & Organisation: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  6. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Transaction Management, Concurrency Control
  7. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling
  8. Digital Logic & Circuits: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Pushdown Automata & CFG, Turing Machines, Moore & Mealy Machines
  10. 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. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Data Warehousing & Mining
  12. Introduction to Emerging Trends: Emerging Tech Trends
  13. Digital Society & Cyber Law: Society, Law & Ethics
  14. HPSC PGT Previous Year Paper:
  15. HPSC Assistant Professor Previous Year Paper:
  16. Live Sessions: HPSC Live Sessions, EMRS TGT/PGT Live Class
  17. Full Mock Test:
  18. HPSC PGT - MOCK Test Series:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment focuses on solving practice problems in graph theory, specifically concerning the relationship between a simple graph G and its complement Gc. The instructor demonstrates how to calculate the number of vertices or edges using fundamental formulas involving complete graphs.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces a problem where a simple graph G has 30 edges and its complement Gc has 36 edges, asking for the number of vertices n. The visible text displays the question 'Q A simple graph G has 30 edges and Gc has 36 edges, the number of vertices in G will be?'. The instructor writes the core formula |E(G)| + |E(Gc)| = n(n-1)/2, representing the total edges in a complete graph. Substituting 30 + 36 = n(n-1)/2, the instructor derives the quadratic equation n^2 - n = 132. The solution process involves factoring: n^2 - 12n + 11n - 132 = 0, leading to n(n-12) + 11(n-12) = 0, and finally (n+1)(n-12) = 0. The instructor notes x = -1 as a rejected solution, implying n=12 is the valid vertex count.

  2. 2:00 – 2:29 02:00-02:29

    The second problem asks to find the number of edges in the complement |E(Gc)| given a simple graph G with |V|=8 and |E|=12. The instructor calculates the total possible edges for a complete graph with 8 vertices using the formula 8(8-1)/2, which equals 28. The visible calculation shows the subtraction step: 28 - 12, resulting in a final answer of 16. This value is circled on the screen as the solution for |E(Gc)|.

The lecture effectively demonstrates two distinct applications of the complement graph edge formula. The first example requires solving a quadratic equation to find the number of vertices n when given edge counts for both G and Gc. The second example is a direct arithmetic application where the total edges of a complete graph are calculated and the known edges of G are subtracted to find the complement's edge count. Both problems rely on the foundational concept that |E(G)| + |E(Gc)| equals n(n-1)/2.

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