A graph G is an ordered triple set {(V(G), E(G), )} consisting of non-empty set V(G) of vertices
A graph G is an ordered triple set {(V(G) 1:45 AM
Definition:1.1
A
graph G is an ordered triple set {(V(G),
E(G),
)} consisting of non-empty set V(G) of vertices, a set E(G)
distinct from V(G) of edges and an incidence function
that associates with edge of G. If e is an
edge and (u,v) are vertices such that
, then e is said to join the vertices u and v and u and v are called the ends of e.
Fig 1.1
Definition:1.2
A
graph is said to be simple if it has
no loops and no multiple or parallel edges.
Fig 1.2
Definition:1.3
An edge (a set of two elements) is drawn as a
line connecting two vertices, called endpoints
or end vertices.
An edge with end vertices x and
y is denoted by xy. The edge set of G is usually denoted by E(G). The size of
a graph is the number of its edges, i.e.
|E(G)|.
Definition:1.4
More
than one edge associated with a given pair of vertices. Such edge referred as parallel edges or multiple edges.
Fig 1.3
Definition:1.5
Two vertices are said to be adjacent
if they are the end vertices of same edge. If
a vertex v is
an end vertex of an edge e,
we say that the vertex v is incident on the edge e and also the edge e is
incident
on vertex v.
