GRAPH THEORY Keijo Ruohonen (Translation by Janne Tamminen, Kung-Chung Lee and Robert Piché) 2008 Contents 1 I DEFINITIONS AND FUNDAMENTAL CONCEPTS 1 1.1 Definitions 6 1.2 Walks, Trails, Paths, Circuits, Connectivity, Components 10 1.3 Graph Operations 14 1.4 Cuts 18 1.5 Labeled Graphs and Isomorphism 20 II TREES 20 2.1 Trees and Forests 23 2.2 (Fundamental) Circuits and (Fundamental) Cut Sets 27 III DIRECTED GRAPHS 27 3.1 Definition 29 3.2 Directed Trees 32 3.3 Acyclic Directed Graphs 34 IV MATRICES AND VECTOR SPACES OF GRAPHS 34 4.1 Matrix Representation of Graphs 36 4.2 Cut Matrix 40 4.
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