Theoretical and Experimental DNA Computation (Natural ...

Fig. 2.7. Fragment of county map
2.5 Data Structures 35
The graph representing this map is depicted in Fig. 2.8, with vertices representing
counties and edges representing borders.
Cornwall
Devon
Somerset Wiltshire
Dorset
Berkshire
Hampshire
Fig. 2.8. Graph representing county map
Isle of Wight
Vertices and edges may have labels attached to them (for example, a vertex
may be labelled with the name of a county, and an edge may be labelled with
the length of the border.) Vertices may be isolated (i.e., be unconnected to
any other vertex). For example, in Fig. 2.7, the Isle of Wight is an island, so
the vertex representing it is isolated. In addition, edges may be directed or
undirected. As their name suggests, the former have an implied direction (if,
for example, they represent one-way streets or flights between two airports),
while the latter have no particular direction attached to them.
Another graph is is presented in Fig. 2.9. As we denote a graph by
G =(V,E), where V is the vertex set and E theedgeset,Fig.2.9represents
the graph G =({v0,v1,v2,v3,v4}, {e0,e1,e2,...,e7}). We denote the
number of vertices in a graph by n =|V | and the number of edges by |E|.
We can specify an edge in terms of the two edges it connects (these are
called its end-points. If the end-points of some edge e are vi and vj, then
we can write e = (vi,vj) (as well as e = (vj,vi) if e is undirected). So,
we can define the graph in Fig. 2.9 as G =(V,E),V =({v0,v1,v2,v3,v4}),
E =({(v0,v0), (v0,v1), (v1,v4), (v4,v1), (v1,v3), (v1,v2), (v2,v3), (v3,v4)}).