Define Eular path and Hamilton path with examples. Draw the Hasse diagram for the divisible relation on the set { 1, 2, 5, 8, 16, 32} and find the maximal, minimal, greatest and least element if exist.

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Eular Path:

A simple path in a graph G that passes through every edge once and only once is called eular path. An euler circuit is an Eular path that returns to its starting vertex.

A connected multigraph has an Eular path but not an euler circuit if and only if it has at most (max) two vertices of odd degree.

Eular Path | HAMROCSIT

a → c → d → e → b → d → a → b

Here, it passes throughall edges only once. No edge is repeated

Hamilton Path:

A simple path in a graph G that passes through every vertex exactly once is called a hamilton path.

Hamilton Graph | HAMROCSIT

a, b, c d    or    a, b, d, c

Here, it passes through every vertices and no vertices is repeacted. So, it is hamilton path.

Diagram Part:

Given set, {1, 2, 5, 8, 16, 32}

According to the given question, we have to find the poset for the divisibility.

Let, the set is A

A = {(1, 2), (1, 5), (1, 8), (1, 16), (1, 32), (2, 8), (2, 16), (2, 32), (8, 16), (8, 32), (16, 32)}

So, now the hasse diagram will be

- Hamro CSIT

Here,

Maximum = 5, 32

Greatest = Do not exists

Minimum = 1

Least  = 1

 

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