Basic Terminology of Graph

Duration: 6 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
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  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. 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
  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. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces the foundational terminology of Graph Theory, beginning with the formal definition of a graph G(V, E) as a set of vertices and edges. The instructor establishes that each edge is an unordered pair of vertices, known as end vertices. Visual aids featuring nodes labeled A through G illustrate these abstract concepts. The lesson progresses to define specific edge types, including self-loops and parallel edges, using handwritten annotations like (B,C) to demonstrate the unordered nature of pairs. Subsequent segments classify graphs into Simple Graphs, which lack self-loops and parallel edges, and Multi/Pseudo Graphs, which permit them. Key definitions for adjacent vertices and adjacent edges are also presented alongside diagrams to clarify incidence relationships.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with the formal definition of a graph G(V, E), displayed on screen as consisting of two sets: vertices V and edges E. The instructor explains that an edge ek is identified with an unordered pair (vi, vj) of vertices. Visual evidence includes a slide listing '1. A graph G (V, E) consist of a set off objects V = {V1, V2, V3,...,VN} called vertices' and '2. Each edge ek is identified with an unordered pair (vi, vj) of vertices.' A diagram showing nodes labeled A through G is used to visualize the structure, while the instructor underlines key terms like 'vertices' and 'edges' to emphasize their roles as fundamental components.

  2. 2:00 – 5:00 02:00-05:00

    The instructor transitions to defining specific edge types and relationships. Handwritten annotations (B,C) and (C,B) appear to illustrate that edges are unordered pairs. The screen displays definitions for 'Self-Loop: Edge having the same vertex (vi, vi) as both its end vertices' and 'Parallel Edge: When more than one edge associated with a given pair of vertices.' The lesson further defines 'Adjacent Vertices' as those joined by the same edges and 'Adjacent Edges' as those incident on a vertex. Diagrams accompany these text definitions, with the instructor underlining phrases like 'same vertex' and 'more than one edge' to highlight critical conditions for classification.

  3. 5:00 – 6:14 05:00-06:14

    The final segment classifies graphs based on the presence of self-loops and parallel edges. A table is displayed comparing 'Simple Graph' against 'Multi/Pseudo Graph'. The text indicates that a Simple Graph contains no self-loops and no parallel edges, whereas a Multi/Pseudo Graph allows both. The instructor underlines 'Simple Graph' and its properties to distinguish it from the alternative classification. This section synthesizes previous definitions into a structural taxonomy, using visual cues to reinforce that the absence of loops and parallel edges is the defining characteristic of a simple graph.

The video systematically builds the vocabulary of Graph Theory, moving from abstract definitions to concrete classifications. It begins by establishing that a graph is composed of vertices and edges, where an edge represents an unordered connection between two end vertices. The instructor uses specific examples like (B,C) to clarify that order does not matter in undirected edges. The lecture then introduces exceptions and variations, defining self-loops where an edge connects a vertex to itself and parallel edges where multiple connections exist between the same pair of vertices. Finally, these concepts are organized into a classification system: Simple Graphs exclude both self-loops and parallel edges, while Multi/Pseudo Graphs include them. This progression ensures students understand not just what a graph is, but how variations in edge structure define different types of graphs.

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