Here is the listing of Best reference books on Advanced Graph Theory.
1. “Introduction to Graph Theory” by Douglas B. West
Book Review: This book provides a thorough introduction to graph theory that covers both the aspects i.e understanding the graphs and writing proofs about graphs. Algorithmic work verification is given more emphasis than the complexity of algorithms. The book provides an effective usage of examples, a number of interesting exercises with challenging examples, demonstration of concepts of trees and distances, matchings and factors, connectivity of graphs and paths, coloring of graphs, edges and cycles and planar graphs. This book is very useful for students studying computer science and mathematics.


2. “Graph Theory with Applications to Engineering and Computer Science” by Narsingh Deo
Book Review: This book presents an insight of how graph theory concept is applied in the field of engineering, physical sciences, social sciences, linguistics and many other areas. The books describes how a graph can be used to represent a physical situation involving discrete objects and relationship among them. The topics included are basics, paths and circuits, trees, cut sets and vertices, vector spaces and matrix representation of graphs, graph coloring and covering. The book also includes problems on directed graphs, enumeration of graphs and computer programs.


3. “Graph Theory” by Frank Harary
Book Review: This book covers various concepts related to the subject of graph theory. The book therefore includes the historical background of graph theory where each concept and the result is clarified with the help of diagrams and figures. The book also contains appendices which provide the readers the diagrams of graphs, directed graphs and trees. The book also provides more importance to theorems rather than algorithms and its applications. The book also provides a comprehensive set of graphs in all the areas of graph theory. The book also provides a nice overview in the area of discrete mathematics.


4. “Network Flows: Theory, Algorithms, and Applications” by R. Ahuja, T. Magnanti, and J. Orlin  
5. “Decision Making in Manufacturing Environment Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods” by Rao R Venkata Rao  
6. “Groups Acting on Graphs” by Bela Bollobas, Warren Dicks, M. J. Dunwoody  
7. “Graph Theory : Proceedings of a Conference Held in Lagow, Poland, February 1013, 1981” by M. Borowiecki  
8. “Topics in Combinatorics and Graph Theory: Essays in Honour of Gerhard Ringel” by Rudolf Henn, Rainer Bodendiek  
9. “Schaum’s Outline of Graph Theory” by V. K. Balakrishnan  
10. “Handbook of Graph Theory (Discrete Mathematics and Its Applications)” by Jonathan L. Gross, Jay Yellen  
Sanfoundry Global Education & Learning Series – Best Reference Books!