Properly Colored Connectivity of Graphs
Description
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references.
Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Reviews / Votes
"The book consists of amazingly beautiful concepts and results which are perfect epitomes of structural analysis of graphs and rich with logic, precision and high degree of intuition. The book also opens up new dimensions for further investigations. The authors really deserve much appreciation for the preparation such an amazing book." (Sudev Naduvath, zbMATH 1475.05002, 2022)More details
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Content
1. Introduction.- 2.General Results.- 3. Connectivity Conditions.- 4. Degree Conditions.- 5. Domination Conditions.- 6. Operations on Graphs.- 7..Random Graphs.- 8. Proper k -Connection and Strong Proper Connection.- 9. Proper Vertex Connection and Total Proper Connection.- 10. Directed Graphs.- 11. Other Generalizations.- 12. Computational Complexity.- Bibliography.- Index.
