Nonlinear optimization problems are found at the heart of real-time operations critical infrastructures. These computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these as graph-structured problems, and illustrate how their structure can be exploited level (for parallelizing function/derivative computations) solver linear ...

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and average degree of the vertices of G. Motivated by the work from Sharafdini et al. [R. Sharafdini, H. Panahbar, Vertex weighted...

where n is the number of vertices of the graph G, and λ1,λ2, . . .,λn are its eigenvalues [1, 4, 5]. Two elementary properties of the graph energy are E(G1 ∪G2) = E(G1) + E(G2) for G1 ∪G2 being the graph consisting of two disconnected components G1 and G2, and E(G∪K1) = E(G), where K1 is the graph with a single vertex. Motivated by the success of the graph-energy concept, and in order to extend...

task graph scheduling is a multi-objective optimization and np-hard problem. in this paper a new algorithm on homogeneous multiprocessors systems is proposed. basically, scheduling algorithms are targeted to balance the two parameters of time and energy consumption. these two parameters are up to a certain limit in contrast with each other and improvement of one causes reduction in the other on...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. This note is about the energy of regular graphs. It is shown that graphs that are close to regular can be made regular with a negligible change of the energy. Also a k-regular graph can be extended to a k-regular graph of a slightly larger order with almost the same energy. As an application, it ...

Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-1<...

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...