Recent advancements in graph theory

"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. This book focuses on the latest research in Graph Theory. It provides recent...

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Detalles Bibliográficos
Otros Autores: Shrimali, N. P., editor (editor), Shah, Nita H., editor
Formato: Libro electrónico
Idioma:Inglés
Publicado: Boca Raton, FL : CRC Press 2020.
Edición:1st ed
Colección:Mathematical engineering, manufacturing, and management sciences
Materias:
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009630802306719
Tabla de Contenidos:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • Biography of Editors
  • Contributors
  • Chapter 1: Graceful Labeling for Eight Sprocket Graph
  • 1.1 Introduction
  • 1.2 Main Results
  • 1.3 Concluding Remark
  • Chapter 2: Universal Absolute Mean Graceful Graphs
  • 2.1 Essential Preface
  • 2.2 α-absolute Mean Graceful Graphs Consisting of the Property of Universality
  • 2.2.1 Extreme Vertices in α-absolute Mean Graceful Graph
  • 2.2.2 Universality in the Path Graph
  • 2.2.3 Universality in the Star Graph
  • 2.2.4 Universality in the Coconut Tree Graph
  • 2.2.5 Special Graph Consisting of Universality in Absolute Mean Graceful Labeling
  • Chapter 3: Universal -Graceful Gear Related Graphs
  • 3.1 Introduction
  • 3.2 Universal α-graceful Gear related Graphs
  • Chapter 4: L(2, 1) - Labeling on Jahangir Graph
  • 4.1 Introduction
  • 4.2 Definitions
  • 4.3 Labeling Number of Generalized Jahangir Graph
  • 4.4 Conclusion
  • Chapter 5: V4-Cordial Labeling of Some Ladder and Book Related Graphs
  • 5.1 Introduction
  • 5.2 Basic Definitions
  • 5.3 Existing Results
  • 5.4 Main Results
  • 5.5 Concluding Remarks
  • Chapter 6: SD-Prime Cordial Labeling of Double k-Polygonal Snake Graph
  • 6.1 Introduction
  • 6.2 Main Results
  • 6.3 Conclusions
  • Chapter 7: Edge Product Cordial and Total Edge Product Cordial Labeling of Some Wheel Related Graphs
  • 7.1 Introduction
  • 7.2 Edge Product Cordial Labeling
  • 7.3 Total Edge Product Cordial Labeling
  • 7.4 Results Related to Shadow Graph of Wheel
  • 7.5 Results Related to Splitting Graph of Wheel
  • 7.6 Results Related to Middle Graph of Wheel
  • 7.7 Results Related to Total Graph of Wheel
  • 7.8 Concluding Remarks
  • 7.9 Open Problems
  • Chapter 8: Product Cordial Labeling for the Line Graph of Bistar
  • 8.1 Introduction
  • 8.2 Main Results
  • 8.3 Concluding Remark.
  • Chapter 9: Sum Divisor Cordial Labeling for Vertex Switching of Cycle Related Graphs
  • 9.1 Introduction
  • 9.2 Sum Divisor Cordial Labeling for Vertex Switching of Cycle Related Graphs
  • 9.3 Concluding Remarks
  • Chapter 10: A Few Results on Fibonacci Cordial Labeling
  • 10.1 Introduction
  • 10.1.1 Definition
  • 10.2 Main Results
  • 10.3 Conclusion
  • Chapter 11: Some More Parity Combination Cordial Graphs
  • 11.1 Introduction
  • 11.2 Notations and Definitions
  • 11.3 Main Results
  • 11.4 Conclusion
  • Chapter 12: Total Neighborhood Prime Labeling of Join Graphs
  • 12.1 Introduction and Definitions
  • 12.2 Main Results
  • Chapter 13: Gaussian Vertex Prime Labeling of Some Graphs Obtained from Origami Models
  • 13.1 Introduction
  • 13.1.1 Spiral Ordering of the Gaussian Integers
  • 13.1.2 Origami Models
  • 13.2 Main Results
  • 13.3 Concluding Remark
  • Chapter 14: Vertex Magic Total Labeling of Tensor Product of Cycles
  • 14.1 Introduction
  • 14.2 Calculation of Magic Constant
  • 14.3 The Product CN ⊗ Cn Possesses n Different Cycles of Length n
  • 14.4 Known Results and Methods
  • Chapter 15: Antimagic Labeling of Some Star and Bistar Related Graphs
  • 15.1 Introduction
  • 15.2 Magic Labeling
  • 15.3 Antimagic Labeling
  • 15.4 Some Known Results of Antimagic Labeling
  • 15.5 Our Investigations
  • 15.6 Conclusion and Scope for Further Research
  • Chapter 16: Distance Magic and Distance Antimagic Labeling of Some Product Graphs
  • 16.1 Introduction
  • 16.2 Cartesian Product of C3t and C4
  • 16.3 Direct Product of C3t and C4
  • 16.4 Strong Product of C3t and C4
  • 16.5 Corona Product of C4 and C3t
  • 16.6 Concluding Remark
  • Chapter 17: Graphs from Subgraphs
  • 17.1 Unary Operations on Graphs
  • 17.2 Binary Operations on Subgraphs
  • 17.3 Graphs from Subgraphs
  • 17.3.1 Graphs from Type 1 Adjacency
  • 17.3.2 Graphs from Type 2 Adjacency.
  • 17.3.3 Graphs from Type 4 Adjacency
  • 17.3.4 Graphs from Type 6 Adjacency
  • 17.3.5 Subgraphs of the Line Graph
  • 17.4 Variations in the Adjacency Definition
  • 17.4.1 Union Adjacency
  • 17.4.2 Chord Crossing Adjacency
  • 17.4.3 Incidence Adjacency
  • 17.4.4 Counting based Adjacency
  • 17.4.5 Distance based Adjacency
  • 17.5 Transformation Graphs
  • 17.6 Iteration, Convergence and Completion
  • 17.7 Research Problems
  • Chapter 18: Unit Graphs Having their Domination Number Half their Order
  • 18.1 Unit Graph
  • 18.1.1 Rings R for which γ(G(R))=|R|2
  • 18.1.2 Rings R for which γ(G(R))=|R|−12
  • 18.2 Domination Number of Line Graph of Unit Graph …
  • 18.2.1 Line Graph of Unit Graph
  • Chapter 19: The Pendant Number of Some Graph Products
  • 19.1 Pendant Number of Cartesian Product of Graphs
  • 19.2 Pendant Number of Direct Product of Graphs
  • 19.3 Conclusion
  • Chapter 20: Wiener Index of Tensor Product of Cycle Graph and Some Other Graphs
  • 20.1 Introduction
  • 20.2 Wiener Index of Tensor Product of Cycle Graph and Bipartite Graph
  • 20.3 Wiener Index of Tensor Product of Cycle Graph with Some Non-bipartite Graphs
  • Chapter 21: Wiener Index of Some Zero-Divisor Graphs
  • 21.1 Introduction
  • 21.2 Wiener Index of the Zero-divisor Graph G(Zn)
  • 21.3 Wiener Index of Zero-Divisor Graphs from Direct Product of Rings
  • 21.4 Concluding Remark
  • Chapter 22: Algebraic Signed Graphs: A Review
  • 22.1 Algebraic Graph
  • 22.1.1 Existing Algebraic Graphs
  • 22.2 Signed Graph and its Parameters
  • 22.2.1 Criteria for Balance
  • 22.2.2 Criteria for Consistency
  • 22.2.3 Criteria for Sign-Compatibility
  • 22.3 Algebraic Signed Graph
  • 22.3.1 Existing Algebraic Signed Graphs
  • 22.4 Signed Total Graphs
  • 22.4.1 Balanced Signed Total Graphs
  • 22.5 Signed Unit Graphs
  • Chapter 23: Nullity and Energy of Complete Tripartite Graphs.
  • 23.1 Introduction and Preliminaries
  • 23.2 Nullity of Complete Tripartite Graphs
  • 23.2.1 Techniques for Nullity of Graph
  • 23.2.1.1 Zero-sum Weighting Technique
  • 23.2.1.2 Co-Neighbor Technique
  • 23.3 Energy of Complete Tripartite Graphs
  • 23.4 Conclusion
  • Chapter 24: Some New Results on Restrained Edge Domination Number of Graphs
  • 24.1 Introduction
  • 24.2 Preliminaries
  • 24.3 Characterization of Restrained Edge Domi-Nating Set
  • 24.4 Restrained Edge Domination Number of Star Related Graphs
  • 24.5 Restrained Edge Domination Number of Cycle Related Graphs
  • 24.6 Concluding Remarks
  • Chapter 25: Some New Graph Coloring Problems
  • 25.1 Introduction
  • 25.2 Rainbow Neighbourhoods in Graphs
  • 25.2.1 Rainbow Neighbourhood Number of Some Basic Graph Classes
  • 25.2.2 Rainbow Neighbourhood Number of Graph Oper-ations
  • 25.2.3 Important Observations
  • 25.2.4 Rainbow Neighbourhood Number of Some Cycle Related Graphs
  • 25.2.5 Rainbow Neighbourhood Number of Some Graph Transformations
  • 25.2.6 Rainbow Neighbourhood Number of Graph Prod-Ucts
  • 25.3 J-Coloring of Graphs
  • 25.3.1 J-Colorability of Graph Operations
  • 25.3.2 The Paucity Number of Graphs
  • 25.4 Conclusion
  • Chapter 26: Total Global Dominator Coloring of Graphs
  • 26.1 Introduction
  • 26.2 Bounds for Total Global Dominator Chromatic Number
  • 26.3 Total Global Dominator Chromatic Number for Some Classes of Graphs
  • 26.4 Conclusion
  • Chapter 27: Rainbow Vertex Connection Number of a Class of Triangular Snake Graph
  • 27.1 Introduction
  • 27.2 Rainbow Vertex Connection Number in Selected Graphs
  • 27.3 Conclusions
  • Chapter 28: Hamiltonian Chromatic Number of Trees
  • 28.1 Introduction
  • 28.2 Preliminaries
  • 28.3 A Lower Bound for hc(T )
  • 28.4 Theorem 1 vs. [3, Theorem 4]
  • 28.4.1 Special Trees A2k and A2k+1
  • 28.4.2 Broom Trees B2k and B2k+1.
  • 28.5 Concluding Remarks
  • Chapter 29: Some Results On Degree Sum Energy of a Graph
  • 29.1 Introduction
  • 29.2 Main Results
  • 29.3 Conclusion
  • Chapter 30: Randic Energy of Some Graphs
  • 30.1 Introduction
  • 30.2 Randic Energy of Extended m-Shadow Graph
  • 30.3 Randic Energy of Extended m-Splitting Graph
  • 30.4 Randic Energy of Double Cover of Graph
  • 30.5 Randic Energy of Extended Double Cover of Graph
  • 30.6 Concluding Remarks
  • Chapter 31: L-Spectra of Graphs Obtained by Duplicating Graphs Elements
  • 31.1 Introduction
  • 31.2 L-spectra of Graph Obtained by Duplicating Each Vertex by an Edge
  • 31.3 L-spectra of Graph Obtained by Duplicating Each Edge by a Vertex
  • 31.4 Conclusion
  • Index.