Das, Kinkar ChandraMaden, Ayşe DilekÇevik, Ahmet Sinan2023-05-302023-05-302013-12Das, K. C. vd. (2013). “On the spectral radius of bipartite graphs which are nearly complete”. Journal of Inequalities and Applications, 2013.1029-242Xhttps://doi.org/10.1186/1029-242X-2013-121https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/1029-242X-2013-121http://hdl.handle.net/11452/32879For p, q, r, s, t is an element of Z(+) with rt <= p and st <= q, let G = G(p, q; r, s; t) be the bipartite graph with partite sets U = {u(1), ..., u(p)} and V = {v(1),..., v(q)} such that any two edges u(i) and v(j) are not adjacent if and only if there exists a positive integer k with 1 <= k <= t such that (k - 1) r + 1 <= i <= kr and (k - 1) s + 1 <= j <= ks. Under these circumstances, Chen et al. (Linear Algebra Appl. 432: 606-614, 2010) presented the following conjecture: Assume that p <= q, k < p, vertical bar U vertical bar = p, vertical bar V vertical bar = q and vertical bar E(G)vertical bar = pq - k. Then whether it is true that lambda(1)(G) <= lambda(1)(G(p, q; k, 1; 1)) = root pq - k + root p(2)q(2) - 6pqk + 4pk + 4qk(2) - 3k(2)/2. In this paper, we prove this conjecture for the range min(vh is an element of V){deg v(h)} <= left perpendicular p-1/2right perpendicular.eninfo:eu-repo/semantics/openAccessMathematicsBipartite graphAdjacency matrixSpectral radiusEigenvaluesConjecturesBoundsProofArticle0003179924000012-s2.0-848943222672013Mathematics, appliedMathematicsSignless Laplacian; Eigenvalue; Signed Graph