On the spectral radius of bipartite graphs which are nearly complete

Das K. C., CANGÜL İ. N., Maden A. D., ÇEVİK A. S.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-121
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: bipartite graph, adjacency matrix, spectral radius, EIGENVALUES, CONJECTURES, BOUNDS, PROOF
  • Bursa Uludag University Affiliated: Yes

Abstract

For 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: