Graph theory, as a recognized discipline, is a relative newcomer to mathematics. The first formal paper is found in the work of Leonard Euler in 1736. In recent years the subject has grown so rapidly that in today's literature, graph theory papers abound with mathematical developments and significant applications. As with any academic field, it is good to step back occasionally and ask ''Where is all this activity taking us?'', ''What are the outstanding fundamental problems?'', ''What are the next important steps to take?'' In short, ''Quo vadis, graph theory?''. The contributors to this volume aim, together, to provide a comprehensive reference source for future directions and open questions in the field.