13.1 Practice Question

Duration: 2 min

This video lesson is available to enrolled students.

Inside: a video lesson and guided study material.

Module outline

About Course: About the Course
Paper 1 | General Studies: State Wise GK / राज्यवार सामान्य ज्ञान (GK)
Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
Paper 1 | Current Affairs: GK- Current Affairs / GK- समसामयिकी
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
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
Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References, Generic & Collections
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
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
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
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
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
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
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
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
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
Paper 2 | Full Length Mock Tests:

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

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.
2:00 – 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.