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...

In this paper, we discuss a generalization of Balakrishnan skew-normal distribution with two parameters that contains the skew-normal, the Balakrishnan skew-normal and the two-parameter generalized skew-normal distributions as special cases. Furthermore, we establish some useful properties and two extensions of this distribution. 

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

let $d$ be a digraph with skew-adjacency matrix $s(d)$‎. ‎the skew‎ ‎energy of $d$ is defined as the sum of the norms of all‎ ‎eigenvalues of $s(d)$‎. ‎two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎we establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energ...

for a finite field $mathbb{f}_q$, the bivariate skew polynomial ring $mathbb{f}_q[x,y;rho,theta]$ has been used to study codes cite{xh}. in this paper, we give some characterizations of the ring $r[x,y;rho,theta]$, where $r$ is a commutative ring. we investigate 2-d skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $r[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ a...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

let $g$ be a simple graph with an orientation $sigma$‎, ‎which ‎assigns to each edge a direction so that $g^sigma$ becomes a‎ ‎directed graph‎. ‎$g$ is said to be the underlying graph of the‎ ‎directed graph $g^sigma$‎. ‎in this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with rand'c weight‎, ‎the skew randi'c matrix ${bf‎ ‎r_s}(g^sigma)$‎, ‎of $g^sigma$ as the real skew symmetric mat...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

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...