# t05_y2008 - The University of Sydney MATH2969/2069 Graph...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The University of Sydney MATH2969/2069 Graph Theory Tutorial 5 (Week 12) 2008 1. ( i ) Let G be the disconnected planar graph shown. Draw its dual G * , and the dual of the dual ( G * ) * . ( ii ) Show that if G is a disconnected planar graph, then G * is connected. Deduce that ( G * ) * is not isomorphic to G . G 2. A certain polyhedron has faces which are triangles and pentagons, with each triangle surrounded by pentagons and each pentagon surrounded by triangles. If every vertex has the same degree, p say, show that 1 e = 1 p- 7 30 . Deduce that p = 4, and that there are 20 triangles and 12 pentagons. Can you construct such a polyhedron? State the dual result. 3. Determine the chromatic number of each of the following graphs: a b c d e f g ( i ) a b c d e f g h i j k ( ii ) a b c d e f g h i j k l ( iii ) a b c d e f g ( iv ) 4. For each of the following graphs, what does Brooks Theorem tell you about the chromatic number of the graph? Find the chromatic number of each graph....
View Full Document

## This document was uploaded on 03/20/2011.

### Page1 / 2

t05_y2008 - The University of Sydney MATH2969/2069 Graph...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online