In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

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...

The D-eigenvalues {μ1, μ2, . . . , μn} of a graph G are the eigenvalues of its distance matrix D and form the D-spectrum of G denoted by specD(G) . The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. We describe here the distance spectrum of some self-complementary graphs in the terms of their adjacency spectrum. These results are used to show that there ex...

The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...

The concept of a consecutive-d digraph was proposed by Du, Hsu and Hwang as a generalization of de Bruijn digraphs, Kautz digraphs, and their generalizations given by Imase and Itoh and Reddy, Pradhan and Kuhl. In this paper we determine the connectivity of consecutive-d digraphs and study how to modify consecutive-d digraphs to reach maximum connectivity. Our results will generalize and improv...

it is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. in this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.

Tournaments are without doubt the best studied class of directed graphs [3, 6]. The generalizations of tournaments arise in order to extend the well-known results on tournaments to more general classes of directed graphs. Moreover, the knowledge about generalizations of tournaments has allowed to deepen our understanding of tournaments themselves. The semicomplete digraphs, the semicomplete mul...