Determine if graph 2 has an Euler circuit, an Euler path but not an Euler circui
ID: 3672679 • Letter: D
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.