Graphs may be classified in many ways apart from their order. A complete graph has each distinct pair of vertices connected by an edge. Many interesting problems arise in looking at complete graphs, several of which have to do with determining whether or not it is possible to pass through every vertex and edge once and only once (a Peterson cycle). A connected graph allows movement from any ver...

Course number: 0366.3267. When and where: Wednesdays 15-18, Ornstein 111. Prospective audience: the course is intended for second and third year undergraduate students in Mathematics or Computer Science. Prerequisites: first year courses in mathematics, most notably Discrete Mathematics or Introduction to Combinatorics. Requirements and grade: Homeworks will be given once every two-three weeks;...

These notes have not been checked by Prof. A.G. Thomason and should not be regarded as ocial notes for the course. In particular, the responsibility for any errors is mine please email Sebastian Pancratz (sfp25) with any comments or corrections.

This book contains the successful invited submissions [1–10] to a special issue of Symmetry on the subject area of ‘graph theory’. Although symmetry has always played an important role in graph theory, in recent years, this role has increased significantly in several branches of this field, including, but not limited to: Gromov hyperbolic graphs, metric dimension of graphs, domination theory, a...

This is a replacement paper. Some of the conclusions from statistical graph theory are reiterated in the sixth section, but not fully resolved therein. Most of the redundancies in the later sections have been deleted. An important number-theoretical technique in the opening section relates to one of the main techniques in the last (sixth) section.

This development provides a formalization of directed graphs, supporting (labelled) multi-edges and infinite graphs. A polymorphic edge type allows edges to be treated as pairs of vertices, if multi-edges are not required. Formalized properties are i.a. walks (and related concepts), connectedness and subgraphs and basic properties of isomorphisms. This formalization is used to prove characteriz...