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Eulerian trails and circuits: existence and identification

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
existence; circuit; connected; compactexistence; circuit; connected; balancedexistence; neither; connected; compactexistence; neither; connected; balancedNOWMix of allRecommended
Question 1 of 8

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Consider the following unweighted network. The vertices name sites, and the edges represent paths proposed for gravelling between reserve locations

Unweighted network. Vertices in listed order: [Camp | Wetland | Lookout | Bridge | Creek]. Full edge list: Creek–Wetland; Creek–Camp; Wetland–Camp; Bridge–Lookout; Wetland–Lookout; Camp–Lookout.CampWetlandLookoutBridgeCreek
(a)1 mark

Determine the number of vertices whose degree is odd

(b)1 mark

Select the statement justified by connectedness and vertex parity