k-ordered Graphs & Out-arc Pancyclicity on Digraphs

Introduction In this part, we shall consider finite graphs without loops and multiple arcs. In the first chapter, we present the basic terminology and notation of graph theory which will be used throughout this part. Before discussing results related to k-ordered graphs in more detail in the following sections, we will briefly explain the basic definitions and some well-known results of Hamiltonian graphs. Our main source follows that of J.A. Bondy and U.S.R. Murty [14] as well as G. Chartrand and L. Lesniak [16], and we refer the reader to these books for any information not provided here. Special notation and definitions will be defined where needed…