338
Solutions to Exercises
on edges of the subgraph are all less than the weights on all other edges.
In
either case, Kruskal's
algorithm selects first the edges of the sub graph since these have weights smaller than other edges
and there are no circuits among them.
9. (a) If the graph is unweighted, put a weight of 1 on edge e
=
uv
and 2 on every other edge. If the
graph is weighted, ensure (by temporarily changing weights if necessary) that the weights of the
edges different from e are all larger than the weight of e. In either case, if Prim's algorithm starts
at
u
or
v,
it will select e first and, if it starts at any other vertex, then as soon as the first of
u, v
is included in one of the sequence of growing trees (to be specific, suppose this is
u
and the tree
is
'T),
edge e will be selected since it is eligible for selection
('T
U
{e}
is also a tree) and e is the
edge of least weight in the graph.
(b) If the graph is unweighted, put weights of 1 on the edges of the subgraph and 2 on all other edges.
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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