Minimal skew energy of oriented unicyclic graphs with a perfect matching
نویسندگان
چکیده
منابع مشابه
On oriented graphs with minimal skew energy
Let S(Gσ) be the skew-adjacency matrix of an oriented graph Gσ . The skew energy of Gσ is the sum of all singular values of its skew-adjacency matrix S(Gσ). This paper first establishes an integral formula for the skew energy of an oriented graph. Then, it determines all oriented graphs with minimal skew energy among all connected oriented graphs on n vertices with m (n ≤ m < 2(n− 2)) arcs, whi...
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Let $S(G^{sigma})$ be the skew-adjacency matrix of the oriented graph $G^{sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $sigma$ to each of its edges. The skew energy of an oriented graph $G^{sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{sigma})$. Two oriented graphs are said to be skew equienergetic iftheir skew energies...
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Let G be a graph on n vertices and let λ1, λ2, . . . , λn be its eigenvalues. The energy of G is defined as E(G) = |λ1| + |λ2| + · · · + |λn|. For various classes of unicyclic graphs, the graphs with maximal energy are determined. Let P 6 n be obtained by connecting a vertex of the circuit C6 with a terminal vertex of the path Pn−6. For n 7, P 6 n has the maximal energy among all connected unic...
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We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of Θ( √ n) noncospectral unicyclic graphs on n vertices with the same Laplacian energy.
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2014
ISSN: 1029-242X
DOI: 10.1186/1029-242x-2014-486