GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.

Synthesis of High Coercivity Core–Shell Nanorods Based on Nickel and Cobalt and Their Magnetic Properties

Hybrid magnetic nanostructures with high coercivity have immense application potential in various fields. Nickel (Ni) electrodeposited inside Cobalt (Co) nanotubes (a new system named Ni @ Co nanorods) were fabricated using a two-step potentiostatic electrodeposition method. Ni @ Co nanorods were crystalline, and they have an average diameter of 150 nm and length of *15 lm. The X-ray diffraction studies revealed the existence of two separate phases corresponding to Ni and Co. Ni @ Co nanorods exhibited a very high longitudinal coercivity. The general mobility-assisted growth mechanism proposed for the growth of one-dimensional nanostructures inside nano porous alumina during potentiostatic electrodeposition is found to be valid in this case too

On the synthesis and magnetic properties of multiwall carbon nanotube– superparamagnetic iron oxide nanoparticle nanocomposites

Multiwall carbon nanotubes (MWCNTs) possessing an average inner diameter of 150 nm were synthesized by template assisted chemical vapor deposition over an alumina template. Aqueous ferrofluid based on superparamagnetic iron oxide nanoparticles (SPIONs) was prepared by a controlled co-precipitation technique, and this ferrofluid was used to fill the MWCNTs by nanocapillarity. The filling of nanotubes with iron oxide nanoparticles was confirmed by electron microscopy. Selected area electron diffraction indicated the presence of iron oxide and graphitic carbon from MWCNTs. The magnetic phase transition during cooling of the MWCNT–SPION composite was investigated by low temperature magnetization studies and zero field cooled (ZFC) and field cooled experiments. The ZFC curve exhibited a blocking at ∼110 K. A peculiar ferromagnetic ordering exhibited by the MWCNT–SPION composite above room temperature is because of the ferromagnetic interaction emanating from the clustering of superparamagnetic particles in the constrained volume of an MWCNT. This kind of MWCNT–SPION composite can be envisaged as a good agent for various biomedical applications