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Laplacian energy of directed graphs and minimizing maximum outdegree algorithms

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概要 Energy has been studied in mathematical perspective as well as physical perspective for several years ago. In spectral graph theory, the eigenvalues of several kinds of matrices have been studied, of which Laplacian matrix attracted the greatest attention [5]. Recently, in 2009, Adiga considered Laplacian energy of directed graphs using skew Laplacian matrix, in which degree of vertex is considered as total of the out-degree and the in-degree. Since directed graphs play an important role in identifying the structure of web-graphs as well as communication graphs, we consider Laplacian energy of simple directed graphs and find some relations by using the general definition of Laplacian matrix. Unlike in [1], we derived two types of equations for simple directed graphs and symmetric directed graphs with $n ≥2$ vertices by considering out-degree of vertex. Further we consider the class $P(alpha)$ which consists of non isomorphic graphs with energy less than some $alpha$ and find 47 non isomorphic directed graphs for class $P(10)$. Our objective extended to enumerate the structure of directed graphs using the Laplacian energy concept. Minimization maximum outdegree(MMO) algorithm defined in [3] can be used to find the directed graphs with minimum Laplacian energy.

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登録日 2013.06.19
更新日 2015.11.06