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   2. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we give some methods to construct (edge) Zagreb equienergetic graphs and show that there are (edge) Zagreb equienergetic graphs of order n  9.

Let $G=(V,E)$ be a simple graph. The energy of $G$ isthe sum of absolute values of the eigenvalues of its adjacencymatrix $A(G)$.In this paper weconsider the edge energy of $G$ (or energy of line of $G$) which is definedas the absolute values of eigenvalues of edge adjacency matrix of $G$. We study the energy for the line of specific graphs.

The horizontal kinetic energy of the fluid flow, from on-land wind to ocean tidal stream, is one of the most promising sources of the energy. In the field of renewable energies, power extraction from Flow Induced Vibration (FIV) of bluff bodies is a fast growing research area which has seen a great advancement over the last decade. In this study, the FIV energy harvesting potential of a sharp edge square cylinder in two different flow incidences is investigated. The square cylinder, depending on its orientation with respect to the incident flow, demonstrates VIV or galloping types of responses. The results indicate that the square cylinder with a flat side perpendicular to the flow has a galloping type of response. In contrast, the same cylinder with a sharp vertex pointing the flow (diamond configuration) shows a VIV type of response. The hydroelastic efficiency of the resonating square cylinder is significantly higher than that with the galloping type of response. This shows the great advantages of diamond VIV excavators over square galloping harvesters.

edge computing is an evolving approach for the growing computing and networking demands from end devices and smart things. edge computing lets the computation to be offloaded from the cloud data centers to the network edge for lower latency, security, and privacy preservation. Although energy efficiency in cloud data centers has been widely studied, energy efficiency in edge computing has been left uninvestigated. In this paper, a new adaptive and decentralized approach is proposed for more energy efficiency in edge environments. In the proposed approach, edge servers collaborate with each other to achieve an efficient plan. The proposed approach is adaptive, and consider workload status in local, neighboring and global areas. The results of the conducted experiments show that the proposed approach can improve energy efficiency at network edges. e.g. by task completion rate of 100%, the proposed approach decreases energy consumption of edge servers from 1053 Kwh to 902 Kwh.

Let G be a graph with n vertices and m edges. The min-imum edge dominating energy is de, ned as the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of the graph G. In this paper, some lower and upper bounds for the minimum edge dominating energy of graph G are established.

Let $G=(V, E)$ be a simple graph such that $\lambda_1, \ldots, \lambda_n$ be the eigenvalues of $G$. The energy of graph $G$ is denoted by $E(G)$ and is defined as $E(G)=\sum_{i=1}^{n}|\lambda_{i}|$. The edge energy of $G$ is the energy of line graph $G$. In this paper, we investigate the energy and edge energy for two Cayley graphs on the abelian group $\mathbb{Z}_{n}^{4}$, namely, the Sudoku graph and the positional Sudoku graph. Also, we obtain graph energy and edge energy of the complement of these two graphs.

The minimum edge dominating energy of a graph $G$ is defined as the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of $G$. In this paper, for some finite symmetric groups $\Gamma$ and subset $S$ of $\Gamma$, the minimum edge dominating energy of the Cayley graph of the group $\Gamma$, denoted by $Cay(\Gamma, S)$, is investigated.