Question

it is possible to construct a graph with 12 edges such that two of its vertices have degree 3 and remaining vertices have degree 4
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Answer 1

Answer:

Let G12 be a simple graph of 12 vertices, and H12 its complement. It is known that G12 has 7 vertices of degree 10, 2 vertices of degree 9, 1 vertex of degree 8 and 2 vertices of degree 7.

Answer 2

Yes, it is possible to construct a graph with 12 edges such that two of its vertices have degree 3 and the remaining vertices have degree 4.

• An example of such a graph would be a complete bipartite graph with 3 vertices on one side and 4 on the other.
• A graph is a collection of vertices (also known as nodes) and edges (lines connecting the vertices). The degree of a vertex is the number of edges connecting to it.
• It is possible to construct a graph with 12 edges where two of the vertices have degree 3 (3 edges connecting to them) and the remaining vertices have degree 4 (4 edges connecting to them).
• A simple example of this type of graph is a complete bipartite graph, which has two sets of vertices, one set with 3 vertices and another set with 4 vertices, and every vertex in the first set is connected to every vertex in the second set.

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