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Define graph.
G = (V,E). Consistes of V, a nonempty set of vertices (also called nodes) and E, a set of edges.
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Define Endpoint.
One or two vertices ssociated with an edge.
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An edge is aid to connect its
endpoint
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If u and v are vertices of a graph, then ....
{u, v} would be an edge of the graph.
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Define Undirected Graph.
Where the edges are undirected; that is, the order of the vertices in an edge is irrelevant.
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Define Simple Graph.
A graph in which each edge connects two different vertices and where no two edges connect the same pair of vertices.
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Define Multigraph.
A graph in which each edge connects two different vertices and where multiple edges connect the same pair of vertices.
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We would say that the multiple edges a what of a single edge?
multiplicity
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Define Pseudograph.
A graph in which it is possible for edges to have a single vertex as both endpoints. These graphs can have multiple edges.
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When an edge has a single vertex as both endpoints, it is called what?
loops
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Define directed graph.
D = (V, E) consists of a nonempty set of vertices V and a set of directed edges E. Each directed edge is associated with an ordered pair of vertices. The directed edge associated with the ordered pair (u, v) is said to start at u and end at v.
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A directed graph can also be called a what?
Diagraph
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A set of directed edges in a directed graph is called what?
arcs
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Simple directed graphs and directed multigraphs are what?
Analogous to their undirected counterparts.
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Define Mixed Graph.
A graph with directed and undirected edges.
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