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E-raamat: How to Label a Graph

  • Formaat: PDF+DRM
  • Sari: SpringerBriefs in Mathematics
  • Ilmumisaeg: 15-Jun-2019
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030168636
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Sari: SpringerBriefs in Mathematics
  • Ilmumisaeg: 15-Jun-2019
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030168636

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This book depicts graph labelings that have led to thought-provoking problems and conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations. A new labeling with a connection to the four color theorem is described to aid mathematicians to initiate new methods and techniques to study classical coloring problems from a new perspective. Researchers and graduate students interested in graph labelings will find the concepts and problems featured in this book valuable for finding new areas of research.

Arvustused

The writing is crisp, clear and instructive, appropriate for undergraduates with a grasp of graph theory fundamentals. The book is best suited as a companion text to introduce undergraduate students to graph labeling problems, perhaps via a research workshop. (André E. Kézdy, Mathematical Reviews, April, 2020)

1 Introduction
1(6)
1.1 Labeled Graphs
1(2)
1.2 Graph Labelings
3(4)
2 Graceful Labelings
7(14)
2.1 Graceful Graphs
7(5)
2.2 Cyclic Decompositions
12(4)
2.3 Graceful Trees
16(5)
3 Harmonious Labelings
21(8)
3.1 Harmonious Graphs
21(4)
3.2 Harmonious Trees
25(4)
4 Prime Labelings
29(24)
4.1 Prime Graphs
29(6)
4.2 Multi-prime Labelings
35(3)
4.3 Subset Labelings
38(7)
4.4 2-Prime Labelings
45(8)
5 Additive Labelings
53(16)
5.1 Rainbow Additive Labelings
53(6)
5.2 Proper Additive Labelings
59(1)
5.3 Monochromatic Additive Labelings
60(3)
5.4 Proper Sigma Labelings
63(2)
5.5 Rainbow Sigma Labelings
65(1)
5.6 Monochromatic Sigma Labelings
66(3)
6 Zonal Labelings
69(16)
6.1 Zonal Graphs
69(5)
6.2 Zonal Labelings of Cycles
74(4)
6.3 Zonal Labelings of Cubic Maps
78(4)
6.4 Inner Zonal Labelings of Bicubic Maps
82(3)
References 85(2)
Index 87