Given a graph G, let G be an oriented graph of G with the orientation σ and skewadjacency matrix S(G). Then the spectrum of S(G) consisting of all the eigenvalues of S(G) is called the skew-spectrum of G, denoted by Sp(G). The skew energy of the oriented graph G, denoted by ES(G), is defined as the sum of the norms of all the eigenvalues of S(G). In this paper, we give orientations of the Krone...

In this paper, skew ABC matrix and its energy are introduced for digraphs. Firstly, some fundamental spectral features of the digraphs established. Then upper lower bounds presented Further extremal determined attaining these bounds.

Compared with their isoelectronic system ethane, both hydrogen peroxide and hydrazine exhibit a double well torsional energy curve where skew conformers are favored over trans conformers and cis conformers are energy-maximum states. Clearly, the involvement of the lone oxygen and nitrogen pairs, or more specifically, the enhanced stabilizing n→σ* negative hyperconjugation effect and destabilizi...

For a simple digraph G of order n with vertex set {v1, v2, . . . , vn}, let d+i and d − i denote the out-degree and in-degree of a vertex vi in G, respectively. Let D (G) = diag(d+1 , d + 2 , . . . , d + n ) and D−(G) = diag(d1 , d − 2 , . . . , d − n ). In this paper we introduce S̃L(G) = D̃(G)−S(G) to be a new kind of skew Laplacian matrix of G, where D̃(G) = D+(G)−D−(G) and S(G) is the skew-adj...

A new Skew Tolerant Flip-Flop (STFF) that achieves the lowest reported delay and energy-delay product while absorbing up to 54ps of clock skew is described. In addition, a method for characterizing clock skew absorbing flip-flops is presented. This comparison is apples-to-apples because the best previously reported flip-flops [1-4] are fabricated on the same wafer and measured using a common te...