The reflection about the line Y=X is equivalent to the reflection along the X-axis,followed by counter clockwise rotation by θ degrees.Find out the value of θ.
Show that number of pendant vertices in a binary tree is (n+1)/2 ,where n is the number of vertices in the tree.
The number of vertices of odd degree in an undirected graph is even,(N-1) is even. Therefore, n is odd. Let p be the number of pendant vertices. 2+p+3(n- p-1) = 2(n-1) or, 3n-2n-3+4 = 2p or, 2p = n+1 or, P = (n+1)/2 Hence, the number of pendant vertices is (n+1)/2. Also, see : 1.) Graph Theory and Tree 2.) The Reflection about line yx is.......... 3.) Prove that a simple graph with n vertices and k components can have at most 1/2(n-k)(n-k-1) edges. 4.) Show for what condition rotation and scaling are commutative. 5.) Vector in R space 6.) Prove that every tree has at most one perfect matching. 7.) Prove that every tree with 2 or more vertices is 2-chromatic. 8.) Show that every Bi-partite graph is 2 chromatic. 9.) Prove that the number of circular permutations of n different objects is (n-1)! . 10.) State the "Pigeon Hole Principle" and the " Generalised pigeon Hole principle".
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