[NOTE: Please up vote my answer.]
ANSWER :
The maximum number of edges that a graph on 7 vertices can have if it contains no K3 = 10.

Adjacency Matrix for the above graph:

What is the maximum number of edges that a graph on 7 vertices can have if...
What is the maximum possible number of edges in a graph with n vertices if: (a) the graph is simple? (b) the graph is acyclic? (c) the graph is planar? Try to justify your answers. [Hint: first look at graphs with few vertices.] Need a clear answer with good neat handwriting please.
Discrete Mathematics
6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
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