Find the diameters of Kn (Connected graph with n vertices), Km,n
(Bipartite graph with m and...
Find the diameters of Kn (Connected graph with n vertices), Km,n
(Bipartite graph with m and n vertices), and Cn (Cycle graph with n
vertices). For each, clearly explain your reasoning.
G is a complete bipartite graph on 7 vertices.
G is planar, and it has an...
G is a complete bipartite graph on 7 vertices.
G is planar, and it has an Eulerian path. Answer the questions, and
explain your answers.
1. How many edges does G have?
2. How many faces does G have?
3. What is the chromatic number of G?
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...
Let n be a positive integer, and let Hn denote the graph whose
vertex set is...
Let n be a positive integer, and let Hn denote the graph whose
vertex set is the set of all n-tuples with coordinates in {0, 1},
such that vertices u and v are adjacent if and only if they differ
in one position. For example, if n = 3, then (0, 0, 1) and (0, 1,
1) are adjacent, but (0, 0, 0) and (0, 1, 1) are not. Answer the
following with brief justification (formal proofs not
necessary):
a....
Graph Theory
.
While it has been proved that any tree with n vertices must have...
Graph Theory
.
While it has been proved that any tree with n vertices must have
n − 1 edges. Here, you will prove the converse of this statement.
Prove that if G = (V, E) is a connected graph such that |E| = |V |
− 1, then G is a tree.