Question 1

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $K _ { 4 }$

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Question 2

The picture at the right shows the ﬂoor plan of

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Question 3

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $W _ { 5 }$

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Question 4

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $C _ { 7 }$

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Question 5

Give a recurrence relation for $v _ { n } = \text { number of vertices of the graph } Q _ { n } \text {. }$

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Question 6

In $K _ { 3,3 }$ let a and b be any two adjacent vertices. Find the number of paths between a and b of length 5.

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Question 7

Give a recurrence relation for $e _ { n } = \text { the number of edges of the graph } K _ { n }$

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Question 8

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $Q _ { 3 }$

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Question 9

Use Dijkstra's Algorithm to ﬁnd the shortest path length between the vertices a and z in this weighted graph.

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Question 10

Consider the graph at the right. 
(a) Does it have an Euler circuit?
(b) Does it have an Euler path?
(c) Does it have a Hamilton circuit?
(d) Does it have a Hamilton path?

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The answer of Consider the graph at the right. 
(a)...

Question 11

The Math Department has 6 committees that meet once a month. How many different meeting times must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are: C₁={ Allen, Brooks, Marg }, C₂={ Brooks, Jones, Morton }, C₃={ Allen, Marg, Morton } , C₄={ Jones, Marg, Morton }, C₅={ Allen, Brooks }, C₆={ Brooks, Marg, Morton } .

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Question 12

In $K _ { 3.3 }$ let a and b be any two adjacent vertices. Find the number of paths between a and b of length 4.

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Question 13

How many diﬀerent channels are needed for six television stations (A, B, C, D, E, F) whose distances (in miles)
from each other are shown in the following table? Assume that two stations cannot use the same channel
when they are within 150 miles of each other? $$\begin{array} { c c c c c c c } 
& A & B & C & D & E & F \
A & - & 85 & 175 & 100 & 50 & 100 \
B & 85 & - & 125 & 175 & 100 & 130 \
C & 175 & 125 & - & 100 & 200 & 250 \
D & 100 & 175 & 100 & - & 210 & 220 \
E & 50 & 100 & 200 & 210 & - & 100 \
F & 100 & 130 & 250 & 220 & 100 & -
\end{array}$$

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The answer of How many diﬀerent channels are needed for...

Question 14

Consider the graph at the right. 
(a) Does it have an Euler circuit?
(b) Does it have an Euler path?
(c) Does it have a Hamilton circuit?
(d) Does it have a Hamilton path?

Accepted Answer

The answer of Consider the graph at the right. 
(a)...

Question 15

Consider the graph at the right. 
(a) Does it have an Euler circuit?
(b) Does it have an Euler path?
(c) Does it have a Hamilton circuit?
(d) Does it have a Hamilton path?

Accepted Answer

The answer of Consider the graph at the right. 
(a)...

Question 16

Determine whether this graph is planar.

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Question 17

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $K _ { 3.2 }$

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Question 18

Use Dijkstra's Algorithm to ﬁnd the shortest path length between the vertices a and z in this weighted graph.

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Question 19

Determine whether this graph is planar.  an oﬃce. Use graph theory ideas to prove that it
is impossible to plan a walk that passes through
each doorway exactly once, starting and ending at 
A.

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Question 20

Determine whether this graph is planar.

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Quiz 10: Graphs

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for K4K _ { 4 }K4​

The picture at the right shows the ﬂoor plan of

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for W5W _ { 5 }W5​

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for C7C _ { 7 }C7​

Give a recurrence relation for vn= number of vertices of the graph Qn. v _ { n } = \text { number of vertices of the graph } Q _ { n } \text {. }vn​= number of vertices of the graph Qn​.

In K3,3K _ { 3,3 }K3,3​ let a and b be any two adjacent vertices. Find the number of paths between a and b of length 5.

Give a recurrence relation for en= the number of edges of the graph Kne _ { n } = \text { the number of edges of the graph } K _ { n }en​= the number of edges of the graph Kn​

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for Q3Q _ { 3 }Q3​

Use Dijkstra's Algorithm to ﬁnd the shortest path length between the vertices a and z in this weighted graph.

Consider the graph at the right. (a) Does it have an Euler circuit? (b) Does it have an Euler path? (c) Does it have a Hamilton circuit? (d) Does it have a Hamilton path?

In K3.3K _ { 3.3 }K3.3​ let a and b be any two adjacent vertices. Find the number of paths between a and b of length 4.

Consider the graph at the right. (a) Does it have an Euler circuit? (b) Does it have an Euler path? (c) Does it have a Hamilton circuit? (d) Does it have a Hamilton path?

Consider the graph at the right. (a) Does it have an Euler circuit? (b) Does it have an Euler path? (c) Does it have a Hamilton circuit? (d) Does it have a Hamilton path?

Determine whether this graph is planar.

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for K3.2K _ { 3.2 }K3.2​

Use Dijkstra's Algorithm to ﬁnd the shortest path length between the vertices a and z in this weighted graph.

Determine whether this graph is planar. an oﬃce. Use graph theory ideas to prove that it is impossible to plan a walk that passes through each doorway exactly once, starting and ending at A.

Determine whether this graph is planar.

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $K _ { 4 }$

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $W _ { 5 }$

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $C _ { 7 }$

Give a recurrence relation for $v _ { n } = \text { number of vertices of the graph } Q _ { n } \text {. }$

In $K _ { 3,3 }$ let a and b be any two adjacent vertices. Find the number of paths between a and b of length 5.

Give a recurrence relation for $e _ { n } = \text { the number of edges of the graph } K _ { n }$

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $Q _ { 3 }$

In $K _ { 3.3 }$ let a and b be any two adjacent vertices. Find the number of paths between a and b of length 4.

Find the vertex-chromatic number, the edge-chromatic number, and the region-chromatic number for $K _ { 3.2 }$