184a_98w_1e

184a_98w_1e - Math 184A First Hour Exam 30 January 1998 1....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 184A First Hour Exam 30 January 1998 1. (6 pts.) Recall that a cycle of a simple graph is a subgraph consisting of some set { v 1 ,...,v k } of vertices together with the k edges { v 1 ,v 2 } , { v 2 3 } , ... , { v k 1 } . It follows from Exercise 5.5.3 that a connected v -vertex graph that has at least one cycle has at least v edges. (You are not asked to do that.) It can be shown that a connected v -vertex graph that has at least two cycles has at least v + 1 edges. (You are not asked to do that.) One might expect the pattern to continue: at least k cycles implies at least v + k - 1 edges. Show that this doesn’t happen by exhibiting for some v a connected v -vertex simple graph with more than two cycles and only v +1 edges . Be sure to describe the cycles! 2. (a) (8 pts.) How many ways are there to form an ordered/ list of 3 (three) letters from the letters in LAJOLLA (3 L’s, 2 A’s, 1 J, and 1 O), provided no letter can be used
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/18/2009 for the course MATH 184a taught by Professor Staff during the Winter '08 term at UCSD.

Ask a homework question - tutors are online