An isolated vertex is a vertex of degree 0. In the edge probe model, show that...
An isolated vertex is a vertex of degree 0. In the edge probe model, show that the problem of deciding if a graph has an isolated vertex is evasive by constructing an adversary strategy that will make any algorithm query all pairs of vertices.
Homework Answers
As mentioned in the question a vertex is a isolated vertex if it is of a degree 0.
which says,
For a graph G=(V(G),E(G)), a vertex x1∈V(G) is considered Isolated if deg(x1)=0.
so in other words an isolated vertex is a vertex that has no
connection with any other vertex so it is called to be
disconnected
here e is the isolated
vertex.
PROBE GRAPH: a Graph is said to be probe graph if its vertex set can be partitioned in two sets probes (P) and non-probes (N), such that N is independent and new edges can be added between non-probes.
Probe Graph also have other different classes in which the graph is partitioned into two sets of edges so if we take the definition probe graph we can say that deciding if a graph has an isolated vertex is evasive by constructing an adversary strategy that will make any algorithm query all pairs of vertices.
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