Question

math 270A quiz 10 discrete structures

Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions: Please complete each question to the best of your ability. Show work to get full credit. Partially correct work will receive partial credit. Lastly please box your answer. 1. (2 points) Are the following graphs isomorphic? Explain why or why not. 2. (3 points) Find a minimum weight spanning tree of the graph below (either highlight the edges that make up the MST, or draw the MST to the side). State the weight of the MST. -34 36 22 35 422510 18 39 / 65 / -30 3. (3 points) Use the graph to the right to answer the following questions. a. Does the graph have an Euler Tour. b. Does the graph have a Hamiltonian Cycle? C. Is the graph bipartite? 4. (2 points) Find the degree of vertex B. Name any sinks or sources if they exist.

Answer 1

Solis yes, here both the graphs are isomorphic to each other, as both have same number of vertices and edges and each vertices are of same degree, 3. we find the MST 2) using kruskal's algorithen of the given graph as follow- 2208 A ac / 19 23 21 - 30 30 1 of the . Weight MST = 22 +9+ 4 + 30+19+21+23+ 18 - 146 3) at No, since there exist two vertices of odd. degree. b) Mo, this graph does not have a hamiltonian cycle. c> yes, this is a bipartite graph because we can represent this graph as follows- coming 47 encomin outgoing is is f as it has as it has vertex vertex Degree of vertex B=3 here the only source O and the only sink 0.