Incidence and Degree
Incidence
·
Incidence:
o
Incidence in graph theory refers to the
relationship between vertices and edges. It describes how vertices are
connected to edges within a graph.
·
Incident Edges:
o
When a vertex is connected to an edge, we say
that the vertex is incident to that edge.
o
In other words, the edge is said to
"touch" or "connect to" the vertex.
·
Incident Vertices:
o
Conversely, when an edge is connected to
vertices, we say that the edge is incident to those vertices.
·
Adjacent Edges:
o
Edges are said to be adjacent if they connect to
the same vertex. In other words, if two or more edges in a graph meet at the
same vertex, they are considered adjacent edges.
·
Degree:
o
The degree of a vertex in a graph is the number
of edges that are incident to (connected to) that vertex.
·
Regular Graph:
o
A type of graph in which every vertex has the
same degree, meaning that all vertices in the graph have an equal number of
edges incident to them.
Note: The number of edges incident on a vertex vi
with a self-loop is counted twice.\
