In the present work, KTP crystals have been grown by spontaneous nucleation technique in flux medium using K6P4O13 flux. 0.4-1 °C/h cooling rates were applied in the spontaneous nucleation process. The presence and amount of impurities has been determined by using XRF. The optical transmission spectra of impure KTP crystals in the UV–visible region are discussed. The transmission cut-off is cle...

We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the node-normalized cut (also called cut ratio) and the edge-normalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to these criteria. The energy model that corresponds to the edge-normalized cut differs from the other ...

A cut edge in a graph G is an edge whose removal increases the number of connected components of G. In this paper we determine the maximum number of cut edges in a connected d-regular graph G of order p.

It is already known that for very small edge cuts in graphs, the crossing number of the graph is at least the sum of the crossing number of (slightly augmented) components resulting from the cut. Under stronger connectivity condition in each cut component that was formalized as a graph operation called zip product, a similar result was obtained for edge cuts of any size, and a natural question ...

A classical result in undirected edge-capaciated networks is the approximate optimality of routing (flow) for multiple-unicast: the min-cut upper bound is within a logarithmic factor of the number of sources of the max flow [2, 3]. In this paper we focus on extending this result to a more general network model, where there are joint polymatroidal constraints on the rates of the edges that meet ...

We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of non-terminal nodes (edges) to delete so that the terminal nodes do not have an odd length path between them. In an earlier work, Lokshtanov and Ramanujan showed that both odd multiway node cut and odd multiway edge cut are ...