Discrete Math Final

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Discrete Math Final
2011-12-07 19:35:24
Discrete Math UAB

Vocab and general definitions/forumulas
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  1. Simple Graph
    A graph in which each edge connects two different vertices and where no two edges connect the same pair of vertices. (Only one edge between any two vertices and no sense of direction)
  2. Multigraph
    A simple graph in which there are several edges connecting at least one vertex to another; does not include self loops.
  3. Pseudograph
    A multigraph which includes edges that connect a vertex to itself
  4. Simple Directed Graph
    A simple graph where edges imply a sense of direction
  5. Directed Multigraph
    A graph where each edge implies a direction and multiple edges between vertices exist.
  6. How can you find the maximum number of edges in a graph?
    Where n is the number of edges, (n*(n-1))/2
  7. Adjacent Vertices
    Two vertices that have an edge between them.
  8. Reflexive
    For every element a in the set S, (a,a) is an element in the relation on S called R. (a is an element of S implies (a,a) is an element of R).
  9. Symmetric
    A relation is said to be symmetric if for every element (a, b) in R there also exists an element (b, a).
  10. Anti-Symmetic
    A relation is said to be anti-symmetric if for any element (a,b) in R there does not exist (b,a) unless a = b.
  11. Transitive
    A relation R is said to be transitive if whenever (a, b) is an element of R and (b, c) is an element of R, then (a, c) is an element of R.