Discrete structure. No. 3. Pls. Note: Please provide solution procedures for eac

Question

Discrete structure.

No. 3. Pls. Note: Please provide solution procedures for each question, including any assumptions and conditions 1. Find the transitive closure of the relation R represented by following digraph. 2. Let R be the relation represented in the above digraph in #1, and let s be the symmetric closure of R. Find SoR, and discuss what you can see from the result. 3. Below is a networking model for data centers in multiple cities. Is there an Euler circuit in the graph? Explain the reason for your answer If yes, show such a circuit, if not, can you show an Euler path in the graph? Detroit New York Chicago San Francisco Washington Denver Los Angeles 4. Apply Dijkstra's algorithm to find a shortest path (in mileage) between Miami and San Francisco in the airline system New York San Francisco 451 Los Angeles

Explanation / Answer

There is no euler cicuit, But there is Euler path

There is no euler cicuit because

All vertices are not of even degree therefore Euler Circuits does not exists

Euler Path

Start from NewYork: =

NewYork ---> Detroit-->Chicago-->Washington-->Newyork-->Chicago---->Denver--->SanFrancisco-->LosAngeles-->Denver


WE can see we visited all the edges exactly once hence there is Euler path but not circuit.

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