# Either draw a graph with the given specifications or explai…

Either draw a graph with the given specifications or explain why no such graph exists: A tree with twelve vertices and eleven edges Notes: 1. Write or type your work neatly and completely. 3. Submit a word document or draw by hand a submit a pdf.

In this assignment, we are asked to either draw a graph or explain why no such graph exists given the specifications of a tree with twelve vertices and eleven edges.

First, let us recall the definition of a tree. A tree is an undirected graph without any cycles or loops, where each pair of vertices is connected by exactly one edge. In other words, a tree is a connected acyclic graph.

Now, let’s analyze the given specifications: a tree with twelve vertices and eleven edges. In a tree, the number of edges is always exactly one less than the number of vertices. This property follows from the fact that each edge connects two vertices, and in a tree, all vertices except one (called the root) have exactly one parent vertex.

Therefore, if we were to draw a tree with twelve vertices, we would need eleven edges to satisfy this property. However, the specifications state that there are only eleven edges. This means that we do not have enough edges to connect all twelve vertices as required for a tree.

Based on this analysis, we can conclude that no such graph exists with the given specifications.

To further illustrate this, let’s assume that we have twelve vertices labeled as V1, V2, … , V12. In a tree, each vertex must be connected to at least one other vertex. Let us start by connecting vertex V1 to some other vertex, say V2. We have used one edge for this connection.

Now, we need to connect V2 to another vertex that is not V1. Let’s connect it to V3 using another edge. We will continue this process, connecting each subsequent vertex (V3, V4, V5, …) to a new vertex until we reach V12.

By connecting the vertices in this manner, we would have used eleven edges to connect all twelve vertices. However, our specifications state that there are only eleven edges, which is not enough to create a tree with twelve vertices. Therefore, no such graph can exist with the given specifications.

In conclusion, it is impossible to draw a graph that satisfies the specifications of a tree with twelve vertices and eleven edges, as this would violate the fundamental properties of a tree.