A graph with 24 edges will contain 16 vertices. Let us see how.

Given-

Number of edges = 24

Degree of each vertex = 3

Let number of vertices in the graph = n.

Using Handshaking Theorem, we have-

Sum of degree of all vertices = 2 x Number of edges

Substituting the values, we get-

n x 3 = 2 x 24

n = 16

Thus, Number of vertices in the graph = 16.

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How many vertices will the following graphs have if they contain- 24 ...

Start with a cycle of size 12, then for every vertex i in the cycle connect it to i+2 and i-2. This graph has 24 edges and each vertex has degree 4. 3.1K views.

For more information, see How many vertices will the following graphs have if they contain- 24 ...

I found an answer from en.wikipedia.org

Edge coloring - Wikipedia

In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the ... The case that n = 3 gives the well-known Petersen graph. ... For many problems in edge coloring, simple graphs behave differently from ... For instance, the 16-vertex planar graph shown in the illustration has m = 24 edges. In this ...

For more information, see Edge coloring - Wikipedia