11. Let G be a graph with n>= 2 vertices.
a) Prove that if G has at least (n-1) + 1 edges the G is connected.
( 2 )
b) Show that the result in (a) is best possible; that is, for each n>= 2, prove there is a graph with (n- 1)
( 2 )
edges that is not connected.
Please see the attached file.
(a) Prove by contradiction:
We know the number of edges in a complete graph with n nodes is (because in a complete graph, every node is connected to other n-1 nodes, therefore the degree of every node is (n-1), and the total degree of ...
Connectedness, Vertices and Edges are investigated. The solution is detiled and well presented.
Graphs and Vector Calculus
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If all edges of Kn (a complete graph) have been coloured red and blue, how do we show that either the red graph or the blue graph is connected?View Full Posting Details