دانلود کتاب Research Trends in Graph Theory and Applications (Association for Women in Mathematics Series, 25)

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Foreword
Preface
Participants and Affiliations at the Time of the Workshop
Workshop Website
Acknowledgments
Contents
Contributors
1 Finding Long Cycles in Balanced Tripartite Graphs: A First Step
1.1 Introduction
1.2 Background
1.2.1 Degree Conditions
1.2.1.1 Degree Conditions and Hamiltonicity
1.2.1.2 Degree Conditions and Long Cycles
1.2.2 Edge Conditions
1.3 Main Result
References
2 Product Thottling
2.1 Introduction
2.2 Initial Cost Product Throttling for Cops and Robbers
2.3 Product Throttling for Power Domination with No Initial Cost
2.3.1 Graphs with thpd(G)=γ(G)
2.3.2 Cartesian Products
2.3.3 Extreme Values
2.4 Universal Product Throttling
2.4.1 General Observations About thY(G) and thY(G)
2.4.2 Low Values of the Product Throttling Number
2.5 Product Throttling for Standard Zero Forcing
2.5.1 Characterization of th(G)
2.5.2 Low Values of th(G)
2.5.3 High Values of th(G)
2.6 Product Throttling for Cops and Robbers Revisited
2.6.1 General Observations
2.6.2 Chordal Graphs
2.7 Product Throttling for Power Domination Revisited
2.7.1 Determination of thpd(G) for Additional Families of Graphs
2.7.2 The Initial Cost Definition thpd(G)
2.8 Product Throttling for PSD Zero Forcing
2.8.1 Initial Cost Definition th+(G)
2.8.2 No Initial Cost Definition th+(G)
2.9 Comparisons of Product Throttling Numbers
References
3 Analysis of Termatiko Sets in Measurement Matrices
3.1 Introduction
3.2 Preliminaries
3.3 Connections Between Termatiko Sets and Other Structures
3.4 Redundancy
3.5 Measurement Matrices from Finite Geometries
3.6 Conclusion
References
4 The Threshold Dimension and Threshold Strong Dimension of a Graph: A Survey
4.1 Introduction
4.2 Background and Preliminaries
4.2.1 The Metric Dimension of a Graph
4.2.2 The Strong Dimension
4.3 Geometric Interpretations for the Threshold Dimension and the Threshold Strong Dimension of a Graph
4.4 Trees
4.5 Bounds
4.5.1 Bounds on the Threshold Dimension of a Graph
4.5.2 Bounds on Threshold Strong Dimension of a Graph
4.6 Irreducible Structures
4.6.1 Irreducible Graphs of Given Order and Dimension
4.7 Concluding Remarks and Open Problems
References
5 Symmetry Parameters for Mycielskian Graphs
5.1 Introduction
5.2 Mycielskian Construction
5.3 Distinguishing and Determining Mycielskians
5.3.1 An Isolated Vertex in Twin-Free G
5.3.2 Isolated Vertices in G with Twins
5.4 Open Problems
References
6 Reconfiguration Graphs for Dominating Sets
6.1 Introduction
6.2 Previous Work on Reconfiguration of Dominating Sets
6.3 Properties of D(G)
6.4 Hamilton Paths in Dominating Graphs
6.4.1 Hamilton Paths in D(Km,n)
6.4.2 Hamilton Paths in D(Pn)
6.5 Additional Results and Future Work
References