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The books of [Bapat 2010] or [Godsil and Royle 2013] are excellent sources for more details on graphs and matrices. Spectrum of the graph also plays an important role in studying "zeta function" on graphs (see [Terras 2010]) and uses what is known as the non-backtracking matrix of a graph.
A PDF document with major definitions and theorems of graph theory, covering topics such as matchings, connectivity, planar graphs, colorings, extremal graph theory, Ramsey theory, flows, and Hamiltonian cycles. The notes are based on the book Graph Theory by Reinhard Diestel and are intended for students of KIT.
Figure 1.1: A drawing of the graph G= (V,E) with vertex set V = {1,2,...,9}and edge set E= {12,13,14,23,45,46,48,56,68,79}. Given a graph G= (V,E), we write |G|for |V|, and e(G) for |E|. We call |G|the order or G, and we call e(G) the size of G. We also want to discuss when a graph is ‘contained’ in some bigger graph. Formally,
Graph Theory lecture notes. 1 De nitions and examples. 1{1 De nitions. De nition 1.1. A graph is a set of points, called vertices, together with a collection of lines, called edges, connecting some of the points. The set of vertices must not be empty.
GRAPH THEORY. Tero Harju. Department of Mathematics University of Turku FIN-20014 Turku, Finland e-mail: harju@utu.fi. 1994 – 2011. Contents. 1 Introduction.......................................................... 2 1.1 Graphs and their plane figures...................................... 4 1.2 Subgraphs
Introduction to Graph Theory. (Chapters 1.1, 1.3–1.6, Appendices A.2–A.3) Prof. Tesler. Math 154 Winter 2020. Related courses. Math 184: Enumerative combinatorics. For two quarters of Combinatorics, take Math 154 and 184 in either order. Math 158 and 188: More advanced/theoretical than Math 154 and 184.
The full lecture notes (PDF - 1.4MB) and the notes by topic below were written by the students of the class based on the lectures and edited with the help of Professor Yufei Zhao. Used with permission. This section includes a full lecture notes and 8 lecture notes by topics.
