Transitive Closure

The transitive closure of a graph G connects u and v iff there is a path in G from u to v. It provides the information called the reachability in a graph. That is, can one get from node a to node d in one or more hops? It is written in matrix form. The graph is given in the form of adjacency matrix, say A[u][v], where A[u][v] is 1 iff there is an edge from vertex u to v, otherwise 0.

Summary

The transitive closure of a graph G connects u and v iff there is a path in G from u to v. It provides the information called the reachability in a graph. That is, can one get from node a to node d in one or more hops? It is written in matrix form. The graph is given in the form of adjacency matrix, say A[u][v], where A[u][v] is 1 iff there is an edge from vertex u to v, otherwise 0.

Things to Remember

  1. The transitive closure of a graph G connects u and v iff there is a path in G from u to v.
  2. It provides the information called the reachability in a graph. 
  3.  That is, can one get from node a to node d in one or more hops? It is written in matrix form.
  4. The graph is given in the form of adjacency matrix, say A[u][v], where A[u][v] is 1 iff there is an edge from vertex u to v, otherwise 0.

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Subjective Questions

Q1:

Define chickenpox?


Type: Very_short Difficulty: Easy

Show/Hide Answer
Answer: <p>Chickenpox (varicella) is a viral infection that causes an itchy, blister-like rash.</p>

Q2:

List down the symptoms of the chickenpox?


Type: Short Difficulty: Easy

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Answer: <p>Chickenpox infection usually lasts about five to 10 days. The rash is the telltale indication of chickenpox. Other signs and symptoms, which may appear one to two days before the rash, include:</p>
<p>- Fever</p>
<p>- Loss of appetite</p>
<p>- Headache</p>
<p>- Tiredness and a general feeling of being unwell (malaise)</p>
<p>&nbsp;</p>
<p>Once the chickenpox rash appears, it goes through three phases:</p>
<p>- Raised pink or red bumps (papules), which break out over several days</p>
<p>- Fluid-filled blisters (vesicles), forming from the raised bumps over about one day before breaking and leaking</p>
<p>- Crusts and scabs, which cover the broken blisters and take several more days to heal</p>

Q3:

What are the nursing management for chickenpox andblist down the its complication?


Type: Long Difficulty: Easy

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Answer: <p>Nursing management for chickenpox are:</p>
<ol>
<li>Antipyretic for fever.</li>
<li>Itching may be relieved by systemic antihistamines and or local application of calamine lotion, gentian violet and sponge baths with antiseptic detergent.</li>
<li>If there are a secondary infection or sign of pneumonia give the child penicillin.</li>
<li>If rashes are very itchy and the child can't sleep give promethazine if necessary.</li>
<li>Teach child to applies pressure to a pruritic area rather than scratch it.</li>
<li>Mouth and a perineal region may be treated by rinses ,gargles, and saline soak.</li>
<li>Nails must be cut short.</li>
<li>Isolation of cases for about 6days after an onset of rash.</li>
<li>Remove loose crust that rubs and irritate skin.</li>
</ol>
<p>&nbsp;</p>
<p>Chickenpox is normally a mild disease. But it can be serious and can lead to complications, especially in high-risk people. Complications include:</p>
<p>- Bacterial infections of the skin, soft tissues, bones, joints or bloodstream (sepsis)</p>
<p>- Pneumonia</p>
<p>- Inflammation of the brain (encephalitis)</p>
<p>- Toxic shock syndrome</p>

Q4:

How it can diagnosed and treated?


Type: Short Difficulty: Easy

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Answer: <p>Doctors generally diagnose chickenpox based on the telltale rash.</p>
<p>If there's any doubt about the diagnosis, chickenpox can be confirmed with laboratory tests, including blood tests or a culture of lesion samples.</p>
<p>&nbsp;</p>
<p>No specific treatment is available. Acyclovir accelerates the rate of clinical and skin lesion improvements, to reduce the number of lesions.</p>
<p>_ Cream : apply to lesion every 4-5 hourly daily for 5-10 days after starting at the first sign of attack.</p>
<p>_ Tablets : 20mg/kg/ dose 4 times daily for 5 days. Its administration should be restricted to immunosuppressed who develop chicken pox.</p>

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Transitive Closure

Transitive Closure

  • .The transitive closure of a graph G connects u and v iff there is a path in G from u to v
  • Given a digraph G (V,E), the transitive closure of G is the digraph G* such that
    • G* has the same vertices as G
    • if G has a directed path from u to v (u != v), G* has a directed edge from u to v.
  • The transitive closure provides information about the reachability in a digraph.
  • The reachability matrix is called transitive closure of the graph.
Fig: Transitive closure visualization
Fig 1(a): Transitive Closure Visualization

Fig 1(b): Transitive Closure Visualization
Fig 1(b): Transitive Closure Visualization

  • The graph is given in the form of the adjacency matrix, say A[u][v], where A[u][v] is 1 iff there is an edge from vertex u to v, otherwise 0.

Fig:Finding Transitive Closure
Fig 2:Finding Transitive Closure
References:

1.www.cs.bu.edu/~steng/teaching/.../lecture21.ppt

2.https://en.wikipedia.org/wiki/Transitive_closure

3.Introduction to Algorithms by Clifford Stein, Thomas H. Cormen, Charles E. Leiserson, Ronald L.

Lesson

Graphs

Subject

Computer Engineering

Grade

Engineering

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