On the integral weighted oriented unicyclic graphs with minimum skew energy

Gong, Shi-Cai; Hou, Yaoping; Woo, Ching-Wah; Xu, Guanghan; Shen, Xiaoling

doi:10.1016/j.laa.2013.02.018

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Extremal Oriented Unicyclic Graphs1

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“…Mao and Hou [54] studied the minimal skew energy oriented unicyclic graphs with given number of pendant vertices and girth, which can also be found in [53]. Gong et al [25] considered the integral weighted oriented unicyclic graphs and determined the minimal skew energy. Some other results on the skew energy of oriented unicyclic graphs have been obtained by Dong [20].…”

Section: Extremal Oriented Unicyclic Graphsmentioning

confidence: 99%

A survey on the skew energy of oriented graphs

Li,

Lian

2013

Preprint

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Let G be a simple undirected graph with adjacency matrix A(G). The energy of G is defined as the sum of absolute values of all eigenvalues of A(G), which was introduced by Gutman in 1970s. Since graph energy has important chemical applications, it causes great concern and has many generalizations. The skew energy and skew energy-like are the generalizations in oriented graphs. Let G σ be an oriented graph of G with skew adjacency matrix S(G σ ). The skew energy of G σ , denoted by ES(G σ ), is defined as the sum of the norms of all eigenvalues of S(G σ ), which was introduced by Adiga, Balakrishnan and So in 2010. In this paper, we summarize main results on the skew energy of oriented graphs. Some open problems are proposed for further study. Besides, results on the skew energy-like: the skew Laplacian energy and skew Randić energy are also surveyed at the end.

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Section: Extremal Oriented Unicyclic Graphsmentioning

confidence: 99%