If a graph has 70 vertices, can each vertex have degree 11?
To determine whether each vertex in a graph with 70 vertices can have a degree of 11, we need to consider the degree of each vertex and the total number of edges in the graph.
The degree of a vertex refers to the number of edges connected to that vertex. In a simple undirected graph, the sum of the degrees of all the vertices is equal to twice the number of edges.
Let's assume that every vertex in the graph has a degree of 11. In this case, the sum of the degrees of all the vertices would be 70 * 11 = 770.
However, in any undirected graph, the sum of the degrees is always an even number. This is because each edge contributes to the degree of two vertices. Given that 770 is an odd number, it is not possible for each vertex to have a degree of 11 in a graph with 70 vertices.
Therefore, it is not possible for each vertex in a graph with 70 vertices to have a degree of 11.