I was wondering if someone could check my answers for these problems: 1) Construct a simple graph G with all of the following properties: • G is connected. • G contains an edge whose removal disconnects G. • Every vertex of G has degree equal to 5.

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I was wondering if someone could check my answers for these problems: 1) Construct a simple graph G with all of the following properties: • G is connected. • G contains an edge whose removal disconnects G. • Every vertex of G has degree equal to 5.

Discrete Math
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|dw:1442027403524:dw|
I count 6 edges connected to these vertices (circled) |dw:1442027885574:dw|
or
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Other answers:

Oh, ok. So I just erase one line ?
but then the outer vertices would only have 4 edges
Oh, that's right. Do I use the 2nd graph I have instead?
that won't work either because of the same reason as above that bridge edge makes 2 nodes have 6 connecting edges
this seems to work though |dw:1442028587295:dw|
|dw:1442028753021:dw| the number in each circle represents the degree of each node
where is the curved not allowed to be plugged in?
what do you mean?
I was trying to do this problem: Construct a simple graph on 6 vertices with 12 edges that does not contain K4 as a subgraph. and I did a graph like...|dw:1442028768219:dw|
I was told this was impossible to do.
so I'm reading that K4 is a complete graph with 4 vertices shown on page 3 of this pdf http://www.dehn.wustl.edu/~blake/circles/talks/2009-jan18-Russ_Woodroofe-Graph_Theory.pdf is that the notation your teacher is using?
Oh, I did the problem. I was just asking about the curves. Is there a rule in which they can't be used for the graphs?
I'm still not sure what you mean? In my drawing? or the one you posted?
in general.
Maybe I heard wrong...
the edges can be curved, yes http://www.math.uvic.ca/faculty/gmacgill/guide/M222Graphs.pdf quoting that PDF ` Graphs are usually represented pictorially with a point (or dot) in the plane corresponding to each vertex and a line segment (or curve of some sort) joining the corresponding points for each pair of adjacent vertices.`
Hmm, can you check another problem for me?
alright
2) Find a cycle of length 20 in the following graph:
Since it's a cycle, I'm sure it's supposed to return to its starting point, no?
yeah you have to make a circuit and not repeat vertices
so they want you to find a circuit with 20 edges where you don't repeat vertices
your answer looks great
Thank you for checking my answers.
no problem

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