The edge-tenacity Te(G) of a graph G was defined as Te(G) = min F⊂E(G) {| F | +τ(G− F ) ω(G− F ) } where the minimum is taken over all edge cutset F of G. We define G-F to be the graph induced by the edges of E(G) − F , τ(G − F ) is the number of edges in the largest component of the graph induced by G-F and ω(G−F ) is the number of components of G− F . A set F ⊂ E(G) is said to be a Te-set of ...

The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

The graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises, how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

Two edge-emitting lasers mutually coupled through orthogonal optical injection exhibit square-wave oscillations in their polarization modes. The TE and TM modes within each individual laser are always in antiphase, but the TE mode of one laser leads the TM of the other by the one-way time of flight between lasers. The duty cycle of the square waves is tunable with pump current and coupling stre...

On the Alcator C-Mod tokamak [Phys. Plasmas 1, 1511, (1994)], radial profiles of electron temperature (Te) and density (ne) are measured at the plasma edge with millimeter resolution Thomson scattering [Rev. Sci. Instrum. 72, 1107 (2001)]. Edge transport barriers in the high confinement regime (Hmode) exhibit Te, ne pedestals with typical widths of 2–6 mm, with the Te pedestal on average slight...

In the supplementary material, we provide additional results and discussion of several parts of the main paper. 1. Effects of Non-Idealities In this section, we show simulations for studying the effects of non-idealities of the wedge geometry on edge radiance profiles. These simulations complement the discussion fo Section 4 of the main paper. Figures 1 and 2 show simulations for the effect of ...

X-ray absorption measurements at both the Se and Te K-edges have been performed in binary chalcogenide amorphous (a-) SexTel_ x films. The EXAFS results for the Se K-edge indicate that the number of Se-Se bonds decreases with increasing Te content, while the number of Se-Te bonds increases. However, the bonding configuration of the Te site, which consists of one Se-Te and one Te-Te bond, remain...

By combining scanning tunneling microscopy and spectroscopy, angle-resolved photoemission spectroscopy, and density functional theory band calculations, we directly observe and resolve the one-dimensional edge states of single bilayer (BL) Bi(111) islands on clean Bi(2)Te(3) and Bi(111)-covered Bi(2)Te(3) substrates. The edge states are localized in the vicinity of step edges having an ∼2  nm w...