Question

determine whether the graph has an euler path, an euler circuit, or neither. if the graph has an euler path or euler circuit, use trial and error or fleurys algorithm to find one. a. choose the correct answer below. the graph has an euler circuit. the graph has an euler path (but not an euler circuit) the graph has neither an euler path nor an euler circuit. b. if the graph has an euler path or euler circuit use trial and error or fleurys algorithm to find one starting at f. choose the correct answer below a. f,b,a,c,g,h,f,c,e,g,f,d,b,g b. f,h,g,f,d,b,f,c,a,b,g,h,f,g,e,c,g c. f,d,b,a,c,e,g,h,f d. there is no euler path or euler circuit

Explanation:

Step1: Recall Euler's theorem

A graph has an Euler circuit if all vertices have even degrees. A graph has an Euler path if exactly two vertices have odd degrees.

Step2: Calculate vertex degrees

Count the number of edges incident to each vertex.

• Degree of \(A\): \(4\) (even)
• Degree of \(B\): \(6\) (even)
• Degree of \(C\): \(6\) (even)
• Degree of \(D\): \(3\) (odd)
• Degree of \(E\): \(3\) (odd)
• Degree of \(F\): \(4\) (even)
• Degree of \(G\): \(5\) (odd)
• Degree of \(H\): \(1\) (odd)

Since there are more than two vertices with odd degrees (\(D\), \(E\), \(G\), \(H\)), by Euler's theorem, the graph has neither an Euler path nor an Euler circuit.

Answer:

a. The graph has neither an Euler path nor an Euler circuit.
b. D. There is no Euler path or Euler circuit.