Xueliang Li

This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.

This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.

Graphs are foundational to combinatorics, modeling relationships across disciplines, from communication networks and social systems to molecular biology. This book presents the first comprehensive treatment of extremal problems in edge-colored graphs, a rapidly developing area at the intersection of graph theory, combinatorics, and applied mathematics. Focusing on the existence of rainbow and properly colored subgraphs, the text explores classical and contemporary topics including anti-Ramsey theory, Gallai-Ramsey results, and rainbow Turán-type problems. It offers a unified framework for understanding how coloring constraints affect graph structure, while drawing connections to Latin squares, transversals, and real-world network models. Rich in theory and application, this accessible and in-depth resource serves as both a reference for researchers and a guide for graduate students, bringing together decades of literature into a coherent and insightful narrative.

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.

Foam fractionation is a separation process in which proteins and other amphipathic species adsorb to the surface of bubbles. The bubbles are then removed from the solution in the form of foam at the top of a column. Due to its cost-effectiveness, foam fractionation has the potential for rapid commercial growth, especially in biotechnology. To assist in the widespread adoption of this highly affordable yet powerful process, Foam Fractionation: Principles and Process Design: Provides a systematic explanation of the underlying physics of foam fractionationDiscusses the fundamentals of molecular adsorption to gas liquid interfaces and the dynamics of foamDescribes foam fractionation process intensification strategiesSupplies design guidance for plant-scale installationsContains the latest knowledge of foam fractionation transport processesPresents a case study of the world’s largest commercial foam fractionation plant producing the food preservative NisinFoam Fractionation: Principles and Process Design capitalizes on the authors’ extensive practical experience of foam fractionation and allied processes to give process engineers, industrial designers, chemical engineers, academics, and graduate students alike a greater understanding of the mechanistic basis and real-world applications of foam fractionation.

Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

Foam fractionation is a separation process in which proteins and other amphipathic species adsorb to the surface of bubbles. The bubbles are then removed from the solution in the form of foam at the top of a column. Due to its cost-effectiveness, foam fractionation has the potential for rapid commercial growth, especially in biotechnology. To assist in the widespread adoption of this highly affordable yet powerful process, Foam Fractionation: Principles and Process Design: Provides a systematic explanation of the underlying physics of foam fractionationDiscusses the fundamentals of molecular adsorption to gas liquid interfaces and the dynamics of foamDescribes foam fractionation process intensification strategiesSupplies design guidance for plant-scale installationsContains the latest knowledge of foam fractionation transport processesPresents a case study of the world’s largest commercial foam fractionation plant producing the food preservative NisinFoam Fractionation: Principles and Process Design capitalizes on the authors’ extensive practical experience of foam fractionation and allied processes to give process engineers, industrial designers, chemical engineers, academics, and graduate students alike a greater understanding of the mechanistic basis and real-world applications of foam fractionation.

Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006. The authors begin with an introduction to rainbow connectedness, rainbow coloring, and rainbow connection number. The work is organized into the following categories, computation of the exact values of the rainbow connection numbers for some special graphs, algorithms and complexity analysis, upper bounds in terms of other graph parameters, rainbow connection for dense and sparse graphs, for some graph classes and graph products, rainbow k-connectivity and k-rainbow index, and, rainbow vertex-connection number. Rainbow Connections of Graphs appeals to researchers and graduate students in the field of graph theory. Conjectures, open problems and questions are given throughout the text with the hope for motivating young graph theorists and graduate students to do further study in this subject.