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Recent Advancements in Graph Theory
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 α-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 Dominating 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 Operations
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 Products
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 Randić Energy of Extended m-Shadow Graph
30.3 Randić Energy of Extended m-Splitting Graph
30.4 Randić Energy of Double Cover of Graph
30.5 Randić 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
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