no of edges in undirected graph

Question

Comments

answer is 506

Answer 1

Example : for $V = \left \{ \left ( i,j \right ) \; | \; 1\leq i\leq 4,1\leq j\leq 4 \right \}$

with the condition for edge is $|\text{x co-ordinate difference} | \leq 1 \or |\text{y co-ordinate difference} | \leq 1$ between any two vertices.

 

In QS:  $12*12$ grid,

• $4*10$ = $40$ vertices with degree $5$
• $4$ corner vertices with degree $3$
• $10*10$ = $100$ vertices with degree $8$
• $\sum (\text{degree}) = 40*5+4*3+100*8 = 1012$
• $n(E) = \frac{\sum(\text{degree})}{2} = 506$

Comments

how is 3 vertical lines reachable from red point?i can see only one which is gng up from that.

and for horizontal lines.how n reduced to n-3??

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the two other vertial lines are satisfying |x co-ordinate difference| $\leq$ 1 condition.

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can you tell which horizontal an vertical lines are u talking about here with reference to point (3,5)??