Consider the graphs $K _ { 5 } , K _ { 2,3 } , \text { and } W _ { 5 }$ Which of these graphs have an Euler circuit? Which have an Euler path?

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The Answer is K5 has ﬁve vertices each of degree 4, so it has an Euler circuit (and an Euler path) since all its vertices have even degree. K2,3 has two vertices of degree 3 and three vertices of degree 2, so it does not have an Euler circuit, but it does have an Euler path since it has exactly two vertices of odd degree. W5 has ﬁve vertices of degree 3 and one vertex of degree 5, so it has neither an Euler circuit nor an Euler path since it has more than two vertices of odd degree.

Consider the Graphs K5,K2,3, and W5K _ { 5 } , K _ { 2,3 } , \text { and } W _ { 5 }K5​,K2,3​, and W5​

Consider the Graphs $K _ { 5 } , K _ { 2,3 } , \text { and } W _ { 5 }$