33 votes 33 votes The minimum number of edges in a connected cyclic graph on $n$ vertices is: $n-1$ $n$ $n+1$ None of the above Graph Theory gate1995 graph-theory graph-connectivity easy + – Kathleen asked Oct 8, 2014 recategorized Apr 25, 2021 by Lakshman Bhaiya Kathleen 21.0k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply priyankapatel commented Apr 4, 2020 reply Follow Share But if when the number of vertices given is 2 then the number of edges will be ??? 0 votes 0 votes Chirag Shilwant commented Jul 19, 2020 reply Follow Share @priyankapatel For a Cycle Graph, No of vertices $\geqslant$ 3 0 votes 0 votes Gajanan Purud commented Sep 15, 2023 reply Follow Share Nice 0 votes 0 votes Please log in or register to add a comment.
Best answer 38 votes 38 votes For making a cyclic graph, the minimum number of edges has to be equal to the number of vertices. Gate Keeda answered Oct 9, 2014 edited Apr 25, 2021 by Lakshman Bhaiya Gate Keeda comment Share Follow See all 2 Comments See all 2 2 Comments reply Hira Thakur commented Oct 9, 2023 reply Follow Share for any cycle graph $C_n$ the number of edges =$n$ 0 votes 0 votes Kshyamano commented Jan 10 reply Follow Share every cyclic graph is not a cycle graph 0 votes 0 votes Please log in or register to add a comment.
11 votes 11 votes answer we be "n" because if you add a single edge also in spanning tree it will make a cycle . spanning tree needs n-1 edges, so to make cycle it must have "(n-1)+1 edges . so option B is correct bharti answered Aug 23, 2017 bharti comment Share Follow See all 0 reply Please log in or register to add a comment.
5 votes 5 votes Ans: B eg. triangle, square etc. rishu_darkshadow answered Oct 7, 2017 rishu_darkshadow comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Its mentioned connected cyclic graph. Hence the minimum degree has to be 2. Also minimum degree <= 2(no. of edges) / (no of vertices) 2 <= 2E / V hence option B is the answer rish1602 answered Jun 3, 2021 rish1602 comment Share Follow See all 0 reply Please log in or register to add a comment.