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...

We use Hadamard's determinantal inequality and its generalization to prove some upper bounds on the energy of a graph in terms degrees, average 2-degrees number common neighbors vertices. Also, we an relating one arbitrary subgraph it.

‎Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$‎. ‎Then the energy of‎ ‎$Gamma$‎, ‎a concept defined in 1978 by Gutman‎, ‎is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$‎. ‎Also‎ ‎the Estrada index of $Gamma$‎, ‎which is defined in 2000 by Ernesto Estrada‎, ‎is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$‎. ‎In this paper‎, ‎we compute the eigen...

in the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. for these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. however, by adding or removing some elements or nodes, such methods cannot be utilized. here, an effi...

Let G be a graph with n vertices and m edges. Let λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G, and let μ1, μ2, . . . , μn be the eigenvalues of the Laplacian matrix of G. An earlier much studied quantity E(G) = ∑ni=1 |λi | is the energy of the graph G. We now define and investigate the Laplacian energy as LE(G) = ∑ni=1 |μi − 2m/n|. There is a great deal of analogy between...

The energy, E(G), of a simple graph G is defined to be the sum of the absolute values of the eigen values of G. If G is a k-regular graph on n vertices,then E(G) k+√k(n− 1)(n− k)= B2 and this bound is sharp. It is shown that for each > 0, there exist infinitely many n for each of which there exists a k-regular graph G of order n with k < n− 1 and B2 < . Two graphs with the same number of vertic...