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Material Type: Notes; Class: Math for Liberal Arts; Subject: MGF: Math - General & Finite; University: Valencia Community College; Term: Unknown 1989;
Typology: Study notes
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CLASS DO : Have them try Konigsberg problem on p. 364. Then show graph representation of Konigsberg.
Draw graphs below on board. Tell students to review at home all bold-faced vocabulary words on pages 364-5.
EULER PATH : Is a path between two vertices which passes each edge exactly once. EULER CIRCUIT : Is an Euler Path that starts and ends at the same vertex. EVEN VERTEX : A vertex that has an even number of edges coming out of it. ODD VERTEX : A vertex that has an odd number of edges coming out of it.
Label vertices on graphs above as either even or odd. NOTE: It is a fact that odd vertices come in pairs. Note for instructor: p. 379 # 32 asks for a proof of this fact: reference Solutions Manual. TELL CLASS If an Euler Path exists: Look at a vertex that is not an end or a beginning. That vertex must be even because if a path goes to the vertex then the path must also leave the vertex.
This idea helps us to understand the Euler theorem.
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p. 369 Euler Theorem :
Revisit graphs on first page. Give Euler paths/circuits if they exist (use directional arrows with circled numbers).
CLASS DO : p. 376 # 8, 10
YOU DO : p. 378 # 22 ANSWER for part a) A B C
YOU DO : p. 373 apply Eulerization definition to
YOU DO : p. 378 # 24 NOTE that edges must be added along existing edges.