Math for Liberal Arts
Math for Liberal Arts MGF 1107
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This 2 page Class Notes was uploaded by Adalberto Stoltenberg on Thursday October 29, 2015. The Class Notes belongs to MGF 1107 at Valencia College taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/231218/mgf-1107-valencia-college in Math at Valencia College.
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Date Created: 10/29/15
Have them try Konigsberg problem on p 354 Then show graph representation of Konigsberg KON39IGSBERG GRAPH r n boarol Tell vocabulary words on pages 3545 m EULER PATH Is apath between two Vemees which passes eaeh edge exactly once IS an n EVEN VERTEX A vertex that has an even number of edges coming out ofit ODD VERTEX A vertexthathas an odd number ofedges coming out ofit 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 ofthls fact reference Solutions Manual TELL C S Ifan Euler Path exists Look at a Vertex that is not an end or a beginning 39 path must also leave thevertex This idea helps us to understand the Euler theorem p 369 Luler lheorem A connected graph has an Euler circuit if all vertices are even A as ifall ofthevertices are ven A graph has neither an Euler Path nor an Euler circuit ifthere are more than two odd vertices ui enuiei I 39 arrows with circled numbers p 375 810 YOUDO p 378 22 ANSWER for part a B c D E YOUDO p373 apply Eulen39zan39on de nition to CD YOUDO p 378 24 NOTE that edges must be added along existing edges