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 21.2k 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.