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Journal of Inequalities and Applications

, 2012:211

First Online: 02 October 2012Received: 11 February 2012Accepted: 18 September 2012

Abstract

Let G be a simple graph and G σ Open image in new window be an oriented graph obtained from G by assigning a direction to each edge of G. The adjacency matrix of G is A G Open image in new window and the skew-adjacency matrix of G σ Open image in new window is S G σ Open image in new window. The adjacency spectral radius ρ G Open image in new window of G and the skew-spectral radius ϱ G σ Open image in new window of G σ Open image in new window are defined as the spectral radius of A G Open image in new window and S G σ Open image in new window respectively.

In this paper, we firstly establish a relation between ϱ G σ Open image in new window and ρ G Open image in new window. Also, we give some results on the skew-spectral radii of G σ Open image in new window and its oriented subgraphs. As an application of these results, we obtain a sharp upper bound of the skew-spectral radius of an oriented unicyclic graph.

MSC: 05C50, 15A18.

Keywordsoriented graph skew-adjacency matrix skew-spectral radius unicyclic graph  Download fulltext PDF



Autor: Guang-Hui Xu

Fuente: https://link.springer.com/







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