GATE CSE
First time here? Checkout the FAQ!
x
0 votes
119 views
Which of the following statements is/are TRUE?
[P] Every disconnected graph has an isolated vertex
[Q] A graph is connected if and only if some vertex is connected to all other vertices
[R] The edge set of every closed trail can be partitioned into edge sets of cycles
[S] If a maximal trail in a graph is not closed, then its endpoints have odd degree
asked in Graph Theory by Active (2k points)   | 119 views

1 Answer

0 votes
P)False. Disconnected means not connected. There may or may not be isolated vertex.

Q)False. In a cycle no vertex connected to all other vertices.

R)False. Partition are disjoint subset of a set. That may or may not a cycle.

S)True.If Trail or Walk is not closed, endpoint must contain some odd degree.
answered by Veteran (53.7k points)  
Q) is not true. It is only true for complete graph.

R)is not true. U cannot consider only a perticular graph. General case u have to assume.

If u are confirmed with ur answer give me some pic what u want to tell

i din't get the solution

 

any conclusion?
Even S isnt true. Take a cycle graph with 4 vertices i.e. square ABCD and connect BD. Now, trace the max trail as ABCDB but A doesnt have odd degree.


Top Users May 2017
  1. akash.dinkar12

    3152 Points

  2. pawan kumarln

    1630 Points

  3. sh!va

    1590 Points

  4. Arjun

    1350 Points

  5. Devshree Dubey

    1246 Points

  6. Angkit

    1044 Points

  7. Debashish Deka

    1022 Points

  8. Bikram

    972 Points

  9. LeenSharma

    820 Points

  10. Prashant.

    692 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. pawan kumarln

    256 Points

  2. Ahwan

    232 Points

  3. jjayantamahata

    114 Points

  4. joshi_nitish

    114 Points

  5. Arnab Bhadra

    94 Points


22,731 questions
29,061 answers
65,094 comments
27,625 users