A graph G is said to be regular if every vertex has the same degree. If this1degree is equal to k, then G is k-regular. For example, K4 is 3-regulara) Draw a connected graph with exactly 5 vertices that is 3-regular, or explain why this isnot possibleb) Draw a connected graph with exactly 8 vertices that is 3-regular, or explain why this isnot possible

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Asked Nov 23, 2019
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Discrete math. graph theory . Please answer (a)

A graph G is said to be regular if every vertex has the same degree. If this
1
degree is equal to k, then G is k-regular. For example, K4 is 3-regular
a) Draw a connected graph with exactly 5 vertices that is 3-regular, or explain why this is
not possible
b) Draw a connected graph with exactly 8 vertices that is 3-regular, or explain why this is
not possible
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A graph G is said to be regular if every vertex has the same degree. If this 1 degree is equal to k, then G is k-regular. For example, K4 is 3-regular a) Draw a connected graph with exactly 5 vertices that is 3-regular, or explain why this is not possible b) Draw a connected graph with exactly 8 vertices that is 3-regular, or explain why this is not possible

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Expert Answer

Step 1

K-regular graph means each vertex has k degree.

Step 2

If Graph, H is 3- regular then degree of each vertex in H is 3.

Number of vertices in H is 5.

So, sum of degrees of all vertices will be,

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3x5 15

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Step 3

The number of edges is half of the sum of the degrees of...

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15 2

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