6 6 votes Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$ Graph Theory graph-theory linear-algebra + – ankitgupta.1729 1.3k views answer comment Share Follow Print See all 7 Comments 7 7 Comments reply Show 4 previous comments Shaik Masthan commented May 22, 2019 reply Follow flag @srestha mam, just taking 2 regular of 4 vertex we can prove it by taking examples we can not prove something... for saying something is false, we can use one example, but for saying something is true, we can't do like that 2 2 replyShare Satbir commented May 22, 2019 reply Follow flag So we have to use like mathematical induction ? or soem other concept ? 0 0 replyShare Shaik Masthan commented May 22, 2019 reply Follow flag yes.... taking any k-regular graph, i observed that, if we think in vector form, there are some vectors are repeating. we are trying for rank, so by eliminating duplicates, i am getting as rank k. Even this is also not formal proof 1 1 replyShare Please log in or register to add a comment.
