منابع مشابه
New skew equienergetic oriented graphs
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...
متن کاملOn 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...
متن کاملskew-spectra and skew energy of various products of graphs
given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...
متن کاملSkew Spectra of Oriented Graphs
An oriented graph G is a simple undirected graph G with an orientation σ, which assigns to each edge a direction so that G becomes a directed graph. G is called the underlying graph of G, and we denote by Sp(G) the adjacency spectrum of G. Skew-adjacency matrix S(G) of G is introduced, and its spectrum SpS(G ) is called the skew-spectrum of G . The relationship between SpS(G ) and Sp(G) is stud...
متن کاملSkew Spectra of Oriented Bipartite Graphs
A graph G is said to have a parity-linked orientation φ if every even cycle C2k in G is evenly (resp. oddly) oriented whenever k is even (resp. odd). In this paper, this concept is used to provide an affirmative answer to the following conjecture of D. Cui and Y. Hou [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, The Electronic J. Combin. 20(2):#P19, 2013]: Let G = G(X,Y ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.02.007