Question

Math 1053 Contemporary Mathematics (2) Katherine Ruiz: Chapter 6 Quiz mis Question: 1 pt 4 of 13 or the graph to the right, complete parts (a) through (d) a) Find a Hamilton path that starts at A and ends at H (Use a comma to separate answers as needed) Find a Hamilton path that starts at Hand ends at A (Use a comma to separate answers as needed =) Explain why the graph has no Hamilton path that starts at Choose the correct answer below A. The vertex iis connected to 3 other vertices, and a Hamiton path must start at a vertex that is connected to at most other vertices B. The edge Ci is a bridge of the graph connected to a "loft hair and a right hall one starts at 1 and goes left or right, there is no way to get to the other half of the graph without going through ingan C. The vertex is not part of any Hamiton paths because it is not connected to all of the other vertices. If one starts at one cannot go left or right without passing through another vertex D. The graph is a complete graph with no loops or multiple edges such that any two distinct vertices are connected by an edge 1) Explain why the graph has no Hamilton circuits Choose the correct answer below A No matter where one starts, one would have to cross the bridge twice to visit every vertex and get back to the starting point 8. The graph is a complete graph with no loops or multiple edges such that any two distinct vertices are connected by an edge ick to select your answer(s). Save for Later Type here to search

Answer 1

We know that Hamiltonian path is a path in a connected graph that covers all the vertices of the graph exactly once without repeating the edges.

(A) Hamiltonian path that starts with A and ends at H is

ABEDCIJFKGH

B) Hamiltonian path starts with H and ends with A is

HGKFJICDEBA.

C) why the graph has no Hamiltonian path starting at I?

If we starts with I and wherever we go either left or right then we have to again pass through vertex I to cover all the vertices ( example, IHCKFJ then again we have to go through I to cover the left side vertices of I) So option B is correct.

D) why the graph has no Hamiltonian circuits?

To make a Hamiltonian circuit one has to cross the bridge CI twice whatever path one follow. So it has no Hamiltonian circuits. So option A is correct.