Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Equal opportunity networks, distance-balanced graphs, and Wiener game

Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.

Lead free heterogeneous multilayers with giant magneto electric coupling for microelectronics/microelectromechanical systems applications

Lead free magneto electrics with a strong sub resonant (broad frequency range) magneto electric coupling coefficient (MECC) is the goal of the day which can revolutionise the microelectronics and microelectromechanical systems (MEMS) industry. We report giant resonant MECC in lead free nanograined Barium Titanate–CoFe (Alloy)-Barium Titanate [BTO-CoFe-BTO] sandwiched thin films. The resonant MECC values obtained here are the highest values recorded in thin films/ multilayers. Sub-resonant MECC values are quite comparable to the highest MECC reported in 2-2 layered structures. MECC got enhanced by two orders at a low frequency resonance. The results show the potential of these thin films for transducer, magnetic field assisted energy harvesters, switching devices, and storage applications. Some possible device integration techniques are also discussed

Marine Product Exports of Kerala in the ASEAN India Free Trade Area: Possibilities and Challenges

In the backdrop of issues encountered by the marine product exports from Kerala in the traditional strongholds of the European Union and the United States, there is a need to target newer markets. The ASEAN India Trade in Goods Agreement (TIGA) though proposes to liberalize trade between India and the ASEAN member nations, fails to deliver greater market access for our marine products in the markets of the ASEAN nations. This can be attributed to factors such as the lower prevailing MFN base rate in the ASEAN nations, tariff reduction commitments reciprocated by them being lesser than India’s offers, inclusion of our prominent items of export in the restrictive lists of most of the ASEAN nations etc. Export forecast suggests that this is a market to be reckoned, which in turn stipulates the need to secure greater concessions and preferential treatment for our marine product exports in the ASEAN nations to capitalize on the gains that have been made

Reliable and Damage-Free Estimation of Resistivity of ZnO Thin Films for Photovoltaic Applications Using Photoluminescence Technique

This work projects photoluminescence (PL) as an alternative technique to estimate the order of resistivity of zinc oxide (ZnO) thin films. ZnO thin films, deposited using chemical spray pyrolysis (CSP) by varying the deposition parameters like solvent, spray rate, pH of precursor, and so forth, have been used for this study. Variation in the deposition conditions has tremendous impact on the luminescence properties as well as resistivity. Two emissions could be recorded for all samples—the near band edge emission (NBE) at 380 nm and the deep level emission (DLE) at ∼500 nm which are competing in nature. It is observed that the ratio of intensities of DLE to NBE ( DLE/ NBE) can be reduced by controlling oxygen incorporation in the sample. - measurements indicate that restricting oxygen incorporation reduces resistivity considerably. Variation of DLE/ NBE and resistivity for samples prepared under different deposition conditions is similar in nature. DLE/ NBE was always less than resistivity by an order for all samples.Thus from PL measurements alone, the order of resistivity of the samples can be estimated.