Mathematics Homework Solutions
Problem
#8042

Prove Connectedness

Prove that G with at least
(n-1)(n-2)/2+1 edges is connected, where n is the order of G.


Solution Summary

Connectedness of an expression is proven by contradiction.

Solution
What is this?
By OTA - Overall OTA Rating
Changping Wang, MA - 4.9/5
Purchase Cost Now
$2.19 CAD
Included in Download
  • Plain text response
$2.19 Instant Download
Add to Cart
Why you can trust BrainMass.com
  • Your Information is Secure
  • Best Online Academic Help Service
  • Students find real academic Success
Related Solutions
  • 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 ...
  • Proving connectedness. - Prove that if G is a disconnected graph, the complement graph G^G is connected, and in fact, diam(G^)<=2.
Browse