Question 1163007: N,O,P,Q,R,S,T,U and edge set {{N,P},{N,U},{O,Q},{O,S},{O,T},{P,R},{P,U},{S,T},{S,U}} .
a. What is the degree of vertex Q ?
b. What is the degree of vertex U?
c. How many components does the graph have?
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
This is one way to draw out the graph. The vertices are {N,O,P,Q,R,S,T,U}.
When we write something like edge {N,P}, we mean that there is a line segment or some kind of curve connecting N to P.
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a. What is the degree of vertex Q ?
The degree for vertex Q is 1 as there is only one connection from vertex Q to any other vertex. We have vertex Q connect to vertex O, as the edge {O,Q} shows.
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b. What is the degree of vertex U?
The degree is 3. We have three edges connect vertex U to the vertices N, S and P.
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c. How many components does the graph have?
There are 8 vertices and 9 edges, making a total of 8+9 = 17 components overall.
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
The correct answer to question "c" is one component.
In graph theory, a component, sometimes called a connected component, of an undirected graph is a subgraph in which
any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph.
A graph that is itself connected has exactly one component, consisting of the whole graph.
See this Wikipedia article
https://en.wikipedia.org/wiki/Component_(graph_theory)#:~:text=In%20graph%20theory%2C%20a%20component,additional%20vertices%20in%20the%20supergraph.&text=A%20vertex%20with%20no%20incident%20edges%20is%20itself%20a%20component.
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