Question: Consider the graph shown. 1. Does it have an Euler circuit? 2. Does it have an Euler path? 3. Does it have a Hamilton
Consider the graph shown. 1. Does it have an Euler circuit? 2. Does it have an Euler path? 3. Does it have a Hamilton circuit? 4. Does it have a Hamilton path? b bo g k C h a d e f J m
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In the image youve provided there is a graph with vertices labeled from a to m Lets address each of the provided questions one by one 1 Does it have an Euler circuit An Euler circuit is a circuit in a graph that visits every edge exactly once and starts and ends at the same vertex A connected graph has an Euler circuit if and only if every vertex has an even degree an even number of edges incident to it By looking at the graph in the picture we can observe that vertices b g j and f each have an odd degree 3 5 5 and 3 respectively Since there are vertices with an odd degree the graph does not have an Euler circuit 2 Does it have an Euler path An Euler path is a path in a graph that visits every edge exactly once and does not need to start and end at the same vertex A connected graph has an Euler path if and only if it has exactly zero or two vertices of an odd degree Since this graph has exactly four vertices of odd degree it does not have an Euler path 3 Does it have a ... View full answer
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