UGC NET CSE | December 2004 | Part 2 | Question: 4

Question

The following lists are the degrees of all the vertices of a graph :

1. $1,2,3,4,5$
2. $3,4,5,6,7$
3. $1, 4, 5, 8, 6$
4. $3,4,5,6$

• A. (i) and (ii)
• B. (iii) and (iv)
• C. (iii) and (ii)
• D. (ii) and (iv)

Answer 1

EVERY GRAPH HAS 2 PROPERTIES:

1) SUM OF DEG OF VERTICES IS EVEN

2)SUM OF OF VERTICES IS EQUAL TO TWICE THE NUMBER OF EDGES

1)1+2+3+4+5=15(NOT EVEN(VIOLATING 1ST PROPERTY))

2) 3+4+5+6+7=25(NOT EVEN(VIOLATING 1ST PROPERTY))

3)1+4+5+8+6=24

4)3+4+5+6=18

SO ANS(B)