The safety of people and the security of the vital functions of society are among the core tasks of governments. Various networks, especially transportation networks, are important for human life. Much research has been done to analyse the vulnerability of road networks and most of the methods were based on analysing the topological structure of the network using graph theory. For instance, Dem...

The ultra-precision diamond cutting process exhibits strong size effects due to the ultra-small depth of cut that is comparable with the cutting edge radius. In the present work, we elucidate the underlying machining mechanisms of single crystal cerium under diamond cutting by means of molecular dynamics simulations, with an emphasis on the evaluation of the effect of depth of cut on the cuttin...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

In order to obtain basic information on the improving the surface integrity of machined surfaces, the relationship between the residual stress of cut surfaces and the cutting edge shapes of cutting tools was examined. Dry facing on a lathe was performed with cutting tools that had various nose radiuses and cutting edge roundnesses. The residual stresses of the cut surfaces were measured by X-ra...

For an edge-colored graph G , we call edge–cut M of monochromatic if the edges are colored with same color. The is called monochromatically disconnected any two distinct vertices separated by a edge–cut. connected disconnection number denoted m d ( ) maximum colors that needed in order to make disconnected. We show almost all graphs have numbers equal 1. also obtain Nordhaus–Gaddum-type results...

Foucaud, Krishna and Ramasubramony Sulochana recently introduced the concept of monitoring edge-geodetic sets in graphs, a related graph invariant. These are vertices such that removal any edge changes distance between some pair set. They studied minimum possible size set given graph, which we call number. We show decision problem for number is NP-complete. also give best-possible upper lower b...

Learning Bayesian network structure from large-scale data sets, without any expert-specified ordering of variables, remains a difficult problem. We propose systematic improvements to automatically learn Bayesian network structure from data. (1) We propose a linear parent search method to generate candidate graph. (2) We propose a comprehensive approach to eliminate cycles using minimal likeliho...