HW WK 12: Graphs

Once an answer is submitted, you will be unable to return to this part. Consider the six bridges map. How many vertices have an odd degree in the graph that models the bridges in the map?

0

How many connected components does the following graphs have?

1 Explanation The given graph is connected, so it has only one component.

Find the length of a shortest path between a and z in the given weighted graph.

16

What is the chromatic number of the given graph?

3

How many connected components does the following graphs have?

3 Explanation The graph has three components: the component that looks like a ∨, the component that looks like a ∧, and the isolated vertex.

Once an answer is submitted, you will be unable to return to this part. Consider the bipartite graph Km,n. Find the values of m and n if Km,n has an Euler circuit.

Km,n has an Euler circuit when both m and n are even and m, n > 0.

Once an answer is submitted, you will be unable to return to this part. Consider the following graph: Does the given graph have a Hamilton circuit? (You must provide an answer before moving to the next part.)

NO

Once an answer is submitted, you will be unable to return to this part. Find a shortest path (in mileage) between each of the following pairs of cities in the airline system shown in the following figure. Miami and Los Angeles

The path via Atlanta, Chicago, and Denver is the shortest.

Once an answer is submitted, you will be unable to return to this part. Find a shortest path (in mileage) between each of the following pairs of cities in the airline system shown in the following figure. Boston and San Francisco

The path via Chicago is the shortest.

Once an answer is submitted, you will be unable to return to this part. Consider the following graph: Identify the correct statement from the following:

This graph can have no Hamilton circuit because of the cut edge {c, f}.

Once an answer is submitted, you will be unable to return to this part. Consider the given graph: Is this a planar graph?

YES

Once an answer is submitted, you will be unable to return to this part. Consider the six bridges map. Can someone cross all the bridges shown in this map exactly once and return to the starting point?

YES

dentify the cut vertices of the given graph.

c

Find the strongly connected components of each of these graphs.

{a, b, c, d, f, g, h, i} and {e}

Find the strongly connected components of each of these graphs.

{a, b, e}, {c}, and {d} The cycle b, a, e, b guarantees that these three vertices are in one strongly connected component. Since there is no path from c to any other vertex and there is no path from any other vertex to d, these two vertices are strong components by themselves. Therefore, the strongly connected components are {a, b, e}, {c}, and {d}.

Find the strongly connected components of each of these graphs.

{a}, {b}, {c, d, e}, and {f}