Determine if graph 2 has an Euler circuit, an Euler path but not an Euler circui

Question

Determine if graph 2 has an Euler circuit, an Euler path but not an Euler circuit, or neither. If the graph has a circuit or path, list the vertices in the circuit or path. If a circuit or path does not exist, give a brief explanation why it doesn't exist. Determine if graph 2 has a Hamilton circuit, a Hamilton path but not a Hamilton circuit, or neither. If the graph has a circuit or path, list the vertices in the circuit or path. If a circuit or path does not exist, give a brief explanation why it doesn't exist. Determine the chromatic number for graph 2. Provide a coloring forthe graph. For each color, provide a list of vertices that have been assigned that color.

Explanation / Answer

C)

Chromatic number for graph2 is 4.

'Red' color for ---- > D,H,F,B.

'Black' color for -----> G,C,I.

'Yellow' color for -----> A

'Green' color for -----> E.

B)

Graph2 does not has Hamiltonion circuit or path because,

Hamilton circuit:

A Graph G has hamiltonion circuit if there is a circuit that has all the vertices of G once.

Hamiltonion Path:

A Graph G has hamiltonion path if there is a path that contains all the vertices of G once.

A)

Graph2 does not have Eulers Path but has Eulers Circuit.

Circuit:

E,B,A,E,F,C,E,I,F,A,D,E,H,I,D,G,E.

A path in amultigraph G that includes exactly once all the vertices of G and has different first and last vertices is called an Eulers path.

If this path contains same first and last terminals ,we called it as Eulers Circuit.

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