Prove Connectedness - Prove that G with at least
(n-1)(n-2)/2+1 edges is connected, where n is the order of G.
Real Analysis : Connectedness and Convergent Sequence - Show that A set E subset or equal to R is connected if and only if, for all nonempty disjoint sets A and B satisfying E=A U B there always exists a convergent sequence (x_n)-->x with (x_n) contained i ...
Connectedness - Let G be a graph of order n such that deg(v)>=(n-1)/2. Prove that G is connected.
Graphs : Connectedness and Cycles - 13. Let G be a connected graph with (please see the attachment). Prove that G contains exactly one cycle.
Graphs : Connectedness, Vertices and Edges - 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 ...