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Ars Combinatoria

  • Research article

On the (Laplacian) Spectral Radius of Bipartite Graphs with Given Number of Blocks

Mingqing Zhai1,2, Ruifang Liu3, Jinlong Shu3
1Department of Mathematics, Chuzhou University, Anhui, Chuzhou, 239012, China
2Department of Mathematics, East China Normal University, Shanghai, 200241, China
3 Department of Mathematics, Chuzhou University, Anhui, Chuzhou, 239012, China
  • Published: 31/01/2011

Abstract

The (Laplacian) spectral radius of a graph is the maximum eigenvalue of its adjacency matrix (Laplacian matrix, respectively). Let \(\mathcal{G}(n,k)\) be the set of bipartite graphs with \(n\) vertices and \(k\) blocks. This paper gives a complete characterization for the extremal graph with the maximum spectral radius (Laplacian spectral radius, respectively) in \(\mathcal{G}(n, k)\).

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Citation
Mingqing Zhai, Ruifang Liu, Jinlong Shu. On the (Laplacian) Spectral Radius of Bipartite Graphs with Given Number of Blocks[J], Ars Combinatoria, Volume 098. 311-319. .