CS 374: Additional notes on Graphs

These notes are intended to supplement the lecture slides and existing notes and references on graphs available at our institution (in particular Jeff Erickson’s excellent notes) and else where. I assume that the reader is already familiar with the basics of graphs and their representation via adjacency lists and adjaceny matrices. We will asssume throughout these notes that graphs are represented via adjacency lists. We will also assume that graphs are simple (no loops and parallel edges) unless we explicitly mention otherwise. For the most part n will denote the number of nodes/vertices and m will denote the number of edges of a graph. Graphs have numerous applications in computer science and other areas inlcuding mathematics. Their power comes from their ability to model a wide variety of problems. This leads to a number of interesting algorithmic problems on graphs. There are two consequences of this phenomenon. First, an efficient algorithm for a basic graph problem leads to many applications. Second, some algorithmic problems on graphs turn out to b be intractable. From an algorithm designer’s point of view the following skills are relevant when working with graphs.