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.

I found an answer from www.quora.com

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

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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