Domination in Graphs: Core Concepts (Paperback, 2023)

1. Introduction.- 2. Historic background.- 3. Domination Fundamentals.- 4. Bounds in terms of order and size, and probability.- 5. Bounds in terms of degree.- 6. Bounds with girth and diameter conditions.- 7. Bounds in terms of forbidden subgraphs.- 8. Domination in graph families : Trees.- 9. Domination in graph families: Claw-free graphs.- 10. Domination in regular graphs including Cubic graphs.- 11. Domination in graph families: Planar graph.- 12. Domination in graph families: Chordal, bipartite, interval, etc.- 13. Domination in grid graphs and graph products.- 14. Progress on Vizing's Conjecture.- 15. Sums and Products (Nordhaus-Gaddum).- 16. Domination Games.- 17. Criticality.- 18. Complexity and Algorithms.- 19. The Upper Domination Number.- 20. Domatic Numbers (for lower and upper gamma) and other dominating partitions, including the newly introduced Upper Domatic Number.- 21. Concluding Remarks, Conjectures, and Open Problems.