Null Graph Vs Trivial Graph

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/HPSC-PGT-COMPUTER-SCIENCE/data-structure-algorithms/graph-theory/types-of-graphs-finite-infinite-null-trivial-complete/asset-null-graph-vs-trivial-graph after enrolling

Inside: a video lesson and guided study material.

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, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  13. Digital Society & Cyber Law: Society, Law & Ethics, साइबर सुरक्षा / Cyber Safety and Security
  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 educational video segment, presented by Anchit Jain from LedgerGate Educator, focuses on defining specific types of graphs in graph theory. The primary concepts covered are the 'Null Graph' and the 'Trivial Graph.' The instructor relies heavily on on-screen text definitions and hand-drawn diagrams to explain these abstract concepts. He begins by establishing the criteria for a Null Graph, emphasizing the emptiness of the edge set. He then contrasts this with the Trivial Graph, which represents the minimal case of a graph. The visual presentation includes labeled vertices, mathematical notation for sets, and specific annotations to guide student understanding of these foundational definitions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor defines a Null Graph. The on-screen text states: 'A graph is said to be null if edge set is empty E = {}, that is a graph with only vertices but no edges.' He draws a diagram labeled G1 with three points 'a', 'b', and 'c'. He circles each vertex in red to show presence without connections. He writes 'null graph' in red ink. Crucially, he underlines 'edge set is empty E = {}' in the text to stress that the absence of edges is the defining feature of this graph type.

  2. 2:00 – 2:42 02:00-02:42

    Next, the instructor introduces the Trivial Graph. The text defines it as 'A graph with only one vertex without an edge is called trivial graph. It is the smallest possible.' He draws a single point labeled 'a' and circles it in red. He writes 'null -> trivial' to indicate a conceptual link. He labels this diagram G2. He underlines 'Trivial Graph' and 'smallest possible' in the text. He briefly writes 'G2' and crosses it out. This section emphasizes that a single isolated vertex is the most basic form of a graph.

The lecture effectively differentiates between Null and Trivial graphs by focusing on vertex and edge counts. A Null Graph is shown to have multiple vertices but zero edges, while a Trivial Graph is defined by having exactly one vertex and zero edges. The instructor uses consistent visual cues, such as red circles for vertices and underlining for key definitions, to reinforce the material. This progression helps students understand that while both lack edges, the Trivial Graph is a specific, minimal subset of the Null Graph concept, representing the absolute smallest graph possible in graph theory.

Loading lesson…