Graph theory has abundant examples of NP-complete problems. Non-planar graphs can require more than four colors, for example this graph:. Graph theory has experienced a tremendous growth during the 20th century. Conference on Graph Theory at SSN College of Engineering, Chennai, held during December 18-20, 2014. The energy, E(G), of a simple graph G is defined to be the sum of the absolute values of the eigen values of G.If G is a k-regular graph on n vertices,then E(G)⩽k+ k(n−1)(n−k) =B 2 and this bound is sharp. A Textbook of Graph Theory (2nd ed.) 12. It is shown that for each ϵ>0, there exist infinitely many n for each of which there exists a k-regular graph G of order n with kGraph theory experienced a tremendous growth in the 20th century. The embedded exercises make it a useful reference for a teacher of a graph theory course or a course in which selected topics of graph theory may occur.” (Suzanne Caulk, MAA Reviews, June, 2013) “The book goes from the basics to the frontiers of research in graph theory, with newly ideas emergent, in mathematics or computer science. Intuitively, a problem isin P1 if thereisan efficient (practical) algorithm tofind a solutiontoit.On the other hand, a problem is in NP 2, if it is first efficient to guess a solution and then One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. Download books for free.