Hw06 - SE 3306 Mathematical Foundations of SE Homework 6 Due on – 10am(1)Can a simple graph exist with 15 vertices of degree five Explain ¯(2

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Unformatted text preview: SE 3306 - Mathematical Foundations of SE Homework # 6 Due on 04/17/2007 – 10am (1)Can a simple graph exist with 15 vertices of degree five? Explain! ¯ (2) The complementary graph G of a simple graph G has the same vertices as G. Two ver¯ tices are adjacent in G if and only if they are not adjacent in G. Describe the complement of the two graphs given below. b 11111 00000 1 0 1 0 11111 00000 1 0 1 0 11111 00000 11111 00000 11111 00000 1 0e 11111 00000 1 0 11111 00000 11111 00000 11111 00000 11111 00000 1 0 1 0 1 1 0 c0 d a b 111 1 000 0 11111 00000 1 0 111 1 000 0 1 0 111 000 111 000 111 000 1 0 111 000e 1 0 111 000 111 000 111 1 000 0 1 0 111 1 000 0 1 c0 d a (3) Given the graph below. Find, if possible or justify otherwise,: b 1 0 1 0 1. a walk with 5 vertices 2. a path with 5 vertices 3. a circuit with 5 vertices 4. a simple circuit with 5 vertices a 1 0 1 0 f 11 00 11 00 1 0 1 0 c 1 0 1 0 e 1 0 1 0 d (4) Given the graph below. Find, if possible or justify otherwise,: a 1 0 1 0 i0 1 b j 1 0 1 0 1 0 1 0 1 0 1 0 p 1 0 1 0 m 1 0 1 0 f k c 1 0 1 0 1 0 1 0 1 0 o 1 0 1 0 n 1 0 1 0 1 0 1 0 q 1 0l 1 0 1 0 1 0 g 1 0h 1 0 1. an Euler Circuit d 1 0 1 0 2. a Hamilton Circuit e0 1 1 0 (5) Given the graph below. Find,the shortest path from a to z. Show each iteration of the algorithm. 1 0 1 0 4 b 5 1 0 1 0 d 5 f 1 0 1 0 7 1 0 1 0 a 3 2 3 1 2 4 1 0 1 0 z 1 0 1 0 c 6 1 0 e 1 0 5 1 0 1 0 g (6) Given the graph below. Draw a planar version of the graph and color it with the minimum number of colors. 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 algorithm. 1 0 1 0 (7) Given the graph below. Find the minimum spanning tree. Show each iteration of the a 1 0 1 0 5 3 7 b 1 0 1 0 5 e 4 6 1 1 0 1 0 3 c 2 d 1 0 1 0 1 0 1 0 1 0 1 0 1 0f 1 0 4 4 6 8 4 3 1 0 g 1 0 h 2 1 0 1 0 i ...
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This note was uploaded on 12/12/2009 for the course SE 3306 taught by Professor Nhut during the Spring '09 term at University of Texas at Dallas, Richardson.

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