Practice Question

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/BIHAR-POLYTECHNIC-LECTURER-COMPUTER-SCIENCE/paper-1-discrete-structures-and-theory-of-logic/graph-theory/graph-isomorphism-definition-detection-and-problem-solving/asset-practice-question-19628 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Discrete Mathematics: Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  2. Digital Logic: Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Pipelining, Multiprocessors
  4. Programming: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
  5. Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  6. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  7. Theory of Computation: Grammar, Regular Language Properties, Moore & Mealy Machines, Turing Machines
  8. 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, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  9. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Security
  10. Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, ORDBMS, NoSQL
  11. Computer Networks: Introduction to CN, Data Communication, 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, Application Layer, Hardware basics, Network Security
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment presents a graph theory practice problem focused on counting simple non-isomorphic graphs. The instructor addresses the specific question: 'How many simple non isomorphic graphs are possible with 4 vertices and 2 edges?' The session begins by explicitly defining the problem parameters on the whiteboard, writing |V| = 4 to denote four vertices and |E| = 2 for two edges. The instructor then systematically constructs possible graph configurations to determine the count of unique structures.

Chapters

  1. 0:00 – 1:53 00:00-01:53

    The instructor introduces a graph theory problem asking for the number of simple non-isomorphic graphs with 4 vertices and 2 edges. He begins by defining the parameters, writing |V| = 4 for vertices and |E| = 2 for edges. He then starts drawing the first possible configuration by connecting two vertices, labeled 'a' and 'b', while leaving others isolated. Subsequently, he draws two distinct configurations: one where the edges share a common vertex (forming a path of length 2) and another where the edges are disjoint (two separate edges). He briefly sketches a third possibility with crossing edges but indicates it is isomorphic to the disjoint case, effectively ruling it out as a unique non-isomorphic graph. The handwritten notes indicate the parameters |V|=4 (vertices) and |E|=2 (edges). Three distinct graph diagrams are drawn to show possible non-isomorphic structures.

The core concept taught is the identification of non-isomorphic graphs based on connectivity and edge arrangement. The instructor demonstrates that graph isomorphism depends on structural equivalence rather than visual layout, as shown when a crossing edge configuration was dismissed as equivalent to the disjoint case. Key evidence includes the explicit definition of parameters |V| = 4 and |E| = 2, alongside the visual construction of a path P3 (connected edges) and two disjoint edges. The lesson emphasizes that simple graphs with identical vertex and edge counts can have multiple non-isomorphic forms, requiring systematic enumeration to find the total count.

Loading lesson…