Study of planar graphs, Euler’s formula (v-e+f=2), and applications to polyhedra. Proves K5 and K3,3 are non-planar, discusses faces, and applies Euler’s formula to regular polyhedra including tetrahedron, cube, and dodecahedron.
Comprehensive coverage of trees as connected acyclic graphs and forests. Includes properties of trees (unique paths, vertex degrees), spanning trees, rooted trees with parent-child relationships, and proof that trees have v-1 edges.
Introduction to graph theory starting with the Seven Bridges of K枚nigsberg problem. Covers basic definitions including vertices, edges, adjacency, degree sequences, connected graphs, and graph representations (adjacency lists and matrices).
Comprehensive chapter summary covering logical connectives, quantifiers, proof strategies, and mathematical reasoning. Includes review problems on truth tables, negations, contrapositives, pigeonhole principle, and graph coloring with knights and knaves puzzles.
Detailed study of function properties (injective, image of sets) and relation properties (transitive). Includes formal definitions, propositions with proofs, and corollaries. Covers graph degree, vertices, and the Handshake Lemma applications.