Recent Advancements in Graph Theory

Recent Advancements in Graph Theory

by N. P. Shrimali, Nita H. Shah
Released November 2020
Publisher(s): CRC Press
ISBN: 9781000210200

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Book description

Graph Theory is a branch of discrete mathematics. It has many applications to many different areas of Science and Engineering. This book provides the most up-to-date research findings and applications in Graph Theory.

Table of contents

  1. Cover
  2. Half Title
  3. Series Page
  4. Title Page
  5. Copyright Page
  6. Contents
  7. Preface
  8. Biography of Editors
  9. Contributors
  10. Chapter 1: Graceful Labeling for Eight Sprocket Graph
    1. 1.1 Introduction
    2. 1.2 Main Results
    3. 1.3 Concluding Remark
  11. Chapter 2: Universal Absolute Mean Graceful Graphs
    1. 2.1 Essential Preface
    2. 2.2 α-absolute Mean Graceful Graphs Consisting of the Property of Universality
      1. 2.2.1 Extreme Vertices in α-absolute Mean Graceful Graph
      2. 2.2.2 Universality in the Path Graph
      3. 2.2.3 Universality in the Star Graph
      4. 2.2.4 Universality in the Coconut Tree Graph
      5. 2.2.5 Special Graph Consisting of Universality in Absolute Mean Graceful Labeling
  12. Chapter 3: Universal α-graceful Gear related Graphs
    1. 3.1 Introduction
    2. 3.2 Universal α-graceful Gear related Graphs
  13. Chapter 4: L(2, 1) - Labeling on Jahangir Graph
    1. 4.1 Introduction
    2. 4.2 Definitions
    3. 4.3 Labeling Number of Generalized Jahangir Graph
    4. 4.4 Conclusion
  14. Chapter 5: V4-Cordial Labeling of Some Ladder and Book related Graphs
    1. 5.1 Introduction
    2. 5.2 Basic Definitions
    3. 5.3 Existing Results
    4. 5.4 Main Results
    5. 5.5 Concluding Remarks
  15. Chapter 6: SD-Prime Cordial Labeling of Double k-Polygonal Snake Graph
    1. 6.1 Introduction
    2. 6.2 Main Results
    3. 6.3 Conclusions
  16. Chapter 7: Edge Product Cordial and Total Edge Product Cordial Labeling of Some Wheel related Graphs
    1. 7.1 Introduction
    2. 7.2 Edge Product Cordial Labeling
    3. 7.3 Total Edge Product Cordial Labeling
    4. 7.4 Results related to Shadow Graph of Wheel
    5. 7.5 Results related to Splitting Graph of Wheel
    6. 7.6 Results related to Middle Graph of Wheel
    7. 7.7 Results related to Total Graph of Wheel
    8. 7.8 Concluding Remarks
    9. 7.9 Open Problems
  17. Chapter 8: Product Cordial Labeling for the Line Graph of Bistar
    1. 8.1 Introduction
    2. 8.2 Main Results
    3. 8.3 Concluding Remark
  18. Chapter 9: Sum Divisor Cordial Labeling for Vertex Switching of Cycle related Graphs
    1. 9.1 Introduction
    2. 9.2 Sum Divisor Cordial Labeling for Vertex Switching of Cycle related Graphs
    3. 9.3 Concluding Remarks
  19. Chapter 10: A Few Results on Fibonacci Cordial Labeling
    1. 10.1 Introduction
      1. 10.1.1 Definition
    2. 10.2 Main Results
    3. 10.3 Conclusion
  20. Chapter 11: Some More Parity Combination Cordial Graphs
    1. 11.1 Introduction
    2. 11.2 Notations and Definitions
    3. 11.3 Main Results
    4. 11.4 Conclusion
  21. Chapter 12: Total Neighborhood Prime Labeling of Join Graphs
    1. 12.1 Introduction and Definitions
    2. 12.2 Main Results
  22. Chapter 13: Gaussian Vertex Prime Labeling of Some Graphs Obtained from Origami Models
    1. 13.1 Introduction
      1. 13.1.1 Spiral Ordering of the Gaussian Integers
      2. 13.1.2 Origami Models
    2. 13.2 Main Results
    3. 13.3 Concluding Remark
  23. Chapter 14: Vertex Magic Total Labeling of Tensor Product of Cycles
    1. 14.1 Introduction
    2. 14.2 Calculation of Magic Constant
    3. 14.3 The Product CN ⊗ Cn Possesses n Different Cycles of Length n
    4. 14.4 Known Results and Methods
  24. Chapter 15: Antimagic Labeling of Some Star and Bistar related Graphs
    1. 15.1 Introduction
    2. 15.2 Magic Labeling
    3. 15.3 Antimagic Labeling
    4. 15.4 Some Known Results of Antimagic Labeling
    5. 15.5 Our Investigations
    6. 15.6 Conclusion and Scope for Further Research
  25. Chapter 16: Distance Magic and Distance Antimagic Labeling of Some Product Graphs
    1. 16.1 Introduction
    2. 16.2 Cartesian Product of C3t and C4
    3. 16.3 Direct Product of C3t and C4
    4. 16.4 Strong Product of C3t and C4
    5. 16.5 Corona Product of C4 and C3t
    6. 16.6 Concluding Remark
  26. Chapter 17: Graphs from Subgraphs
    1. 17.1 Unary Operations on Graphs
    2. 17.2 Binary Operations on Subgraphs
    3. 17.3 Graphs from Subgraphs
      1. 17.3.1 Graphs from Type 1 Adjacency
      2. 17.3.2 Graphs from Type 2 Adjacency
      3. 17.3.3 Graphs from Type 4 Adjacency
      4. 17.3.4 Graphs from Type 6 Adjacency
      5. 17.3.5 Subgraphs of the Line Graph
    4. 17.4 Variations in the Adjacency Definition
      1. 17.4.1 Union Adjacency
      2. 17.4.2 Chord Crossing Adjacency
      3. 17.4.3 Incidence Adjacency
      4. 17.4.4 Counting based Adjacency
      5. 17.4.5 Distance based Adjacency
    5. 17.5 Transformation Graphs
    6. 17.6 Iteration, Convergence and Completion
    7. 17.7 Research Problems
  27. Chapter 18: Unit Graphs having their Domination Number half their Order
    1. 18.1 Unit Graph
      1. 18.1.1 Rings R for which γ(G(R))=|R|2
      2. 18.1.2 Rings R for which γ(G(R))=|R|−12
    2. 18.2 Domination Number of Line Graph of Unit Graph …
      1. 18.2.1 Line Graph of Unit Graph
  28. Chapter 19: The Pendant Number of Some Graph Products
    1. 19.1 Pendant Number of Cartesian Product of Graphs
    2. 19.2 Pendant Number of Direct Product of Graphs
    3. 19.3 Conclusion
  29. Chapter 20: Wiener Index of Tensor Product of Cycle Graph and Some Other Graphs
    1. 20.1 Introduction
    2. 20.2 Wiener Index of Tensor Product of Cycle Graph and Bipartite Graph
    3. 20.3 Wiener Index of Tensor Product of Cycle Graph with Some Non-bipartite Graphs
  30. Chapter 21: Wiener Index of Some Zero-Divisor Graphs
    1. 21.1 Introduction
    2. 21.2 Wiener Index of the Zero-divisor Graph G(Zn)
    3. 21.3 Wiener Index of Zero-Divisor Graphs from Direct Product of Rings
    4. 21.4 Concluding Remark
  31. Chapter 22: Algebraic Signed Graphs: A Review
    1. 22.1 Algebraic Graph
      1. 22.1.1 Existing Algebraic Graphs
    2. 22.2 Signed Graph and its Parameters
      1. 22.2.1 Criteria for Balance
      2. 22.2.2 Criteria for Consistency
      3. 22.2.3 Criteria for Sign-compatibility
    3. 22.3 Algebraic Signed Graph
      1. 22.3.1 Existing Algebraic Signed Graphs
    4. 22.4 Signed Total Graphs
      1. 22.4.1 Balanced Signed Total Graphs
    5. 22.5 Signed Unit Graphs
  32. Chapter 23: Nullity and Energy of Complete Tripartite Graphs
    1. 23.1 Introduction and Preliminaries
    2. 23.2 Nullity of Complete Tripartite Graphs
      1. 23.2.1 Techniques for Nullity of Graph
        1. 23.2.1.1 Zero-sum Weighting Technique
        2. 23.2.1.2 Co-neighbor Technique
    3. 23.3 Energy of Complete Tripartite Graphs
    4. 23.4 Conclusion
  33. Chapter 24: Some New Results on Restrained Edge Domination Number of Graphs
    1. 24.1 Introduction
    2. 24.2 Preliminaries
    3. 24.3 Characterization of Restrained Edge Dominating Set
    4. 24.4 Restrained Edge Domination Number of Star related Graphs
    5. 24.5 Restrained Edge Domination Number of Cycle related Graphs
    6. 24.6 Concluding Remarks
  34. Chapter 25: Some New Graph Coloring Problems.
    1. 25.1 Introduction
    2. 25.2 Rainbow Neighbourhoods in Graphs
      1. 25.2.1 Rainbow Neighbourhood Number of Some Basic Graph Classes
      2. 25.2.2 Rainbow Neighbourhood Number of Graph Operations
      3. 25.2.3 Important Observations
      4. 25.2.4 Rainbow Neighbourhood Number of Some Cycle related Graphs
      5. 25.2.5 Rainbow Neighbourhood Number of Some Graph Transformations
      6. 25.2.6 Rainbow Neighbourhood Number of Graph Products
    3. 25.3 J -Coloring of Graphs
      1. 25.3.1 J -colorability of Graph Operations
      2. 25.3.2 The Paucity Number of Graphs
    4. 25.4 Conclusion
  35. Chapter 26: Total Global Dominator Coloring of Graphs
    1. 26.1 Introduction
    2. 26.2 Bounds for Total Global Dominator Chromatic Number
    3. 26.3 Total Global Dominator Chromatic Number for Some Classes of Graphs
    4. 26.4 Conclusion
  36. Chapter 27: Rainbow Vertex Connection Number of a Class of Triangular Snake Graph
    1. 27.1 Introduction
    2. 27.2 Rainbow Vertex Connection Number in Selected Graphs
    3. 27.3 Conclusions
  37. Chapter 28: Hamiltonian Chromatic Number of Trees
    1. 28.1 Introduction
    2. 28.2 Preliminaries
    3. 28.3 A Lower Bound for hc(T )
    4. 28.4 Theorem 1 vs. [3, Theorem 4]
      1. 28.4.1 Special Trees A2k and A2k+1
      2. 28.4.2 Broom Trees B2k and B2k+1
    5. 28.5 Concluding Remarks
  38. Chapter 29: Some Results on Degree Sum Energy of a Graph
    1. 29.1 Introduction
    2. 29.2 Main Results
    3. 29.3 Conclusion
  39. Chapter 30: Randic Energy of Some Graphs
    1. 30.1 Introduction
    2. 30.2 Randić Energy of Extended m-Shadow Graph
    3. 30.3 Randić Energy of Extended m-Splitting Graph
    4. 30.4 Randić Energy of Double Cover of Graph
    5. 30.5 Randić Energy of Extended Double Cover of Graph
    6. 30.6 Concluding Remarks
  40. Chapter 31: L-Spectra of Graphs Obtained by Duplicating Graphs Elements
    1. 31.1 Introduction
    2. 31.2 L-spectra of Graph Obtained by Duplicating Each Vertex by an Edge
    3. 31.3 L-spectra of Graph Obtained by Duplicating Each Edge by a Vertex
    4. 31.4 Conclusion
  41. Index

Product information

  • Title: Recent Advancements in Graph Theory
  • Author(s): N. P. Shrimali, Nita H. Shah
  • Release date: November 2020
  • Publisher(s): CRC Press
  • ISBN: 9781000210200