For given non-abelian group G, the non-commuting (NC)-graph $Gamma(G)$ is a graph with the vertex set $G$ $Z(G)$ and two distinct vertices $x, yin V(Gamma)$ are adjacent whenever $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

Congestion indicates an economic state where inputs are overly invested. Evidence of congestion occurs whenever reducing some inputs can increase outputs. In this paper, we present a new model to identify and evaluate congestion in Data Envelopment Analysis (DEA). We use output efficient DMUs to construct our proposed model to evaluate congestion. We also proposed a linear inequality and equali...

In statistics it is often assumed that sample observations are independent. But sometimes in practice, observations are somehow dependent on each other. Spatiotemporal data are dependent data which their correlation is due to their spatiotemporal locations.Spatiotemporal models arise whenever data are collected across bothtime and space. Therefore such models have to be analyzed in termsof thei...

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.

It was thought previously that cardiac muscle gap junctions provide low-resistance connections between cells and permit the local-circuit current to flow. Some evidences show that myocardial cells may not require low-resistance connections for successful propagation of the action potential (AP). It seems that some other types of mechanisms must be involved in AP propagation. In this article, we...