6 votes 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 asked May 22, 2019 ankitgupta.1729 649 views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments Shaik Masthan commented May 22, 2019 reply Follow Share @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 votes 2 votes Satbir commented May 22, 2019 reply Follow Share So we have to use like mathematical induction ? or soem other concept ? 0 votes 0 votes Shaik Masthan commented May 22, 2019 reply Follow Share 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 votes 1 votes Please log in or register to add a comment.