Recent advancements in graph theory / edited by N. P. Shrimali, Nita H. Shah.

Format:

Book

Contributor:

Shrimali, N. P., editor.

Shah, Nita H., editor.

Series:

Mathematical engineering, manufacturing, and management sciences

Language:

English

Subjects (All):

Graph theory.

Physical Description:

1 online resource (411 pages).

Edition:

1st ed.

Place of Publication:

Boca Raton, FL : CRC Press, 2020.

Summary:

"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 findings that are occurring in the field, offers insights on an international and transnational levels, identifies the gaps in the results, and includes forthcoming international studies and research, along with its applications in Networking, Computer Science, Chemistry, and Biological Sciences, etc. The book is written with researchers and post graduate students in mind"-- Provided by publisher.

Contents:

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.

Notes:

Includes index.

Description based on: online resource; title from pdf title page (COMPUTERSCIENCEnetBase, viewed January 8, 2021)

ISBN:

1-00-303843-3

1-003-03843-3

1-000-21018-9

1-000-21020-0

9781003038436

OCLC:

1176315313