gr-t2 - NAME TEST2/MAD3305 Page 1 of 4 General directions...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
NAME: TEST2/MAD3305 Page 1 of 4 _________________________________________________________________ General directions: Read each problem carefully and do exactly what is requested. Show all your work neatly. Use complete sentences and use notation correctly. Make your arguments and proofs as complete as possible. Remember that what is illegible or incomprehensible is worthless. _________________________________________________________________ 1. (25 pts.) (a) What is a bridge?? [Yes, a definition is required.] (b) Give an example of a graph of order n and size n - 1 that is not a tree. (c) A certain tree of order n has only vertices of degree 3 and degree 1. How many degree 3 vertices does the tree have? (d) If G is a nonseparable graph with order at least 3, what is the best estimate that you provide for δ (G)? Why?? (e) Let T be a tree of order n 2 with k = (G). Let n i be the number of vertices of degree i for 1 i k. Then and . k i 1 n i n 2( n 1) k i 1 in i Show how to obtain a formula for the number of end-vertices of T.
Image of page 1

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

View Full Document Right Arrow Icon
TEST2/MAD3305 Page 2 of 4 _________________________________________________________________ 2. (15 pts.) For the graph G below, determine the cut-vertices, bridges, and blocks of G. List the cut-vertices and bridges in
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern