Consider the graph below. a) Does the graph have an Euler path? If so, find such a path. If it does not, give an argument to show why not such a path exists. b) Does the graph have an Euler circuit? If so, find such circuit. If it does not, give an argument to show why not such a circuit exists. c) Does the graph have a Hamilton path? If so, find such a path. If it does not, give an argument as to why not such a path exists. And d) Does the graph have a Hamilton circuit? If so, find such circuit. If it does not, give an argument as to why not such a circuit exists.
no graph
To determine if the given graph has an Euler path or circuit, we need to analyze its properties. Similarly, to determine if the graph has a Hamilton path or circuit, we need to examine different characteristics. I will guide you through the process.
a) To check for an Euler path, we need to verify if the graph satisfies both of these conditions:
1. The graph is connected.
2. The graph has either zero or two vertices with odd degrees.
Start by examining the graph to determine if it is connected. If any vertices are disconnected, there is no Euler path present.
b) To check for an Euler circuit, we need to verify if the graph satisfies the following conditions:
1. The graph is connected.
2. All vertices have an even degree.
Like in the previous step, examine the graph to determine if it is connected. If any vertices have an odd degree, then there is no Euler circuit.
c) To check for a Hamilton path, we need to verify if the graph contains a path that visits each vertex exactly once.
Begin by examining the graph to see if a path exists that passes through each vertex exactly once. If such a path cannot be found, there is no Hamilton path in the graph.
d) To check for a Hamilton circuit, we need to verify if the graph contains a circuit that visits each vertex exactly once.
Continue examining the graph to determine if a circuit exists that visits every vertex exactly once. If such a circuit cannot be found, there is no Hamilton circuit in the graph.
Please provide the graph so that we can further analyze and answer your questions accurately.