Clearly this geodesic is of order 48.
Evidently, the diameter of G is at least 47.
You could write
this as follows:
diam(G)
≥
47.
(d)
Suppose that G is a graph of order 25 and size 99.
From
this information, we know that any trail in G can be no longer
than what number l?
Provide the best upper bound.
Sorry about the notation, the lower case L.
Trails have to have
distinct edges.
Hence the best bound with the current
information isl=9
9
.
(e)
Suppose that G is a graph of order 25 and size 99.
From
this information, we know that any path in G can be no longer
than what number l?
Provide the best upper bound.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentTEST1/MAD3305
Page 2 of 4
_________________________________________________________________
2. (20 pts.)
Provide mathematical definitions for each of the
following terms.
(a)
A graph G:
A graph G consists of a finite nonempty set V
of vertices and a set E of 2element subsets of V called edges.
[For convenience, we frequently write V as V(G) and E as E(G)
when we are dealing with more than one graph as a time.]
(b)
Subgraph:
A graph H is called a subgraph of a graph G,
written H
⊆
G, if V(H)
⊆
V(G) and E(H)
⊆
E(G).
(c)
Spanning Subgraph:
A subgraph H of a graph G is said to be
a spanning subgraph if the vertex set of H is the same as the
vertex set of G, that is, V(H) = V(G).
(d)
Bipartite Graph:
A graph G is a bipartite graph if there
are nonempty subsets U and W of V(G) with U
∪
W = V(G),
U
∩
W=
φ
, and each edge of G joins a vertex from U and a vertex
from W.
[The sets U and W are called partite sets.]
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '12
 Rittered
 Graph Theory, Vertex, subgraph

Click to edit the document details