MadeEasy Full Length Test 2018: Graph Theory - Counting

Question

The Number of Labelled possible graph given below ?

 

what I did was →

we doesn’t  remove any of the edge out of 4   = $\binom{4}{0}$   [Because a Graph is sub-graph of itself]

we can remove any of one edge out of 4 = $\binom{4}{1}$

we can remove any of the two edges out of 4  = $\binom{4}{2}$

similarly ,  $\binom{4}{3}$ , $\binom{4}{4 }$

then  , add of the them

 

Comments

[Because a Graph is sub-graph of itself]

A subgraph of a graph is a graph whose vertex set and edge set are subsets of those of .

if u are playing with edges then u can also play with vertices. like graph can contain only 1 vertex. ( 4 cases)

or may be combination of vertices and edges like 2 vertex 1 edge etc.

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thanks @Satbir

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What's the final solution then?

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We can also look at this question as finding number of possible subsets of a set.

Let S be a set with all the 4 edges, number of subgraphs possible is the number of subsets of S, so answer should be 16.