DM-Graphs-Q13

+1 vote

A graph contains exactly 2 odd degree vertices, x,y.
Which one of the following statements is always true?

(A). There is a path from x to some even degree vertex which goes through y
(B). There is a path from x to y
(C). There is a path from some even degree vertex to some even degree vertex
(D). There is a path from some even degree vertex to either x or y

asked Jul 12 in Discrete Maths by gbeditor (16,060 points)
reshown Jul 13 by gbeditor

1 Answer

0 votes

Think of a 2 component disconnected graph...

say 1st component is consisting of only 1 vertex with degree 0

and 2nd component has to have 2 odd degree (since a single component cant have odd no. of odd degrees) therefroe there is always a path between them ie x and y but not with the other component having degree 0

 

 

therefore option B

answered Jul 13 by tssoumambanerjee-nit (1,040 points)
Answer:
...