Let G = (V, E) be a tree, and let M be the greatest possible
number...
Let G = (V, E) be a tree, and let M be the greatest possible
number of vertices in a path that is a subgraph of G. Show that any
two paths with M vertices in G must have at least one vertex in
common.
Let T be a complete binary tree such that node v stores
the entry (p(v), 0),...
Let T be a complete binary tree such that node v stores
the entry (p(v), 0), where p(v) is the level number of v. Is tree T
a heap? Why or why not?
I know that a complete binary tree is a heap, but shouldn't we
also take into consideration the values that it is storing into the
tree: (p(v), 0)? The heap tree could be either a min-heap or
max-heap. If we order the the value based of p(v)...
Suppose V is a vector space over F, dim V = n, let T be a...
Suppose V is a vector space over F, dim V = n, let T be a linear
transformation on V.
1. If T has an irreducible characterisctic polynomial over F,
prove that {0} and V are the only T-invariant subspaces of V.
2. If the characteristic polynomial of T = g(t) h(t) for some
polynomials g(t) and h(t) of degree < n , prove that V has a
T-invariant subspace W such that 0 < dim W < n
10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the...
10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the edge set?
Construct a bipartite graph with vertices Q,R,S,T,U,V,W such
that the degree of S is 4.
What is the edge set?
12.-Construct a simple graph with vertices F,G,H,I,J that has an
Euler trail, the degree of F is 1 and the degree of G is 3.
What is the edge set?
13.-Construct a simple graph with vertices L,M,N,O,P,Q that has
an Euler circuit...