Connectivity of Direct Products of Graphs

Let $\kappa(G)$ be the connectivity of $G$ and $G\times H$ the direct product of $G$ and $H$. We prove that for any graphs $G$ and $K_n$ with $n\ge 3$, $\kappa(G\times K_n)=min\{n\kappa(G),(n-1)\delta(G)\}$, which was conjectured by Guji and Vumar.Comment: 5 pages, accepted by Ars Com

Anisotropic thermal expansion of AEFe2As2 (AE = Ba, Sr, Ca) single crystals

We report anisotropic thermal expansion of the parent, AEFe2As2 (AE = Ba, Sr, and Ca), compounds. Above the structural/antiferromagnetic phase transition anisotropy of the thermal expansion coefficients is observed, with the coefficient along the a-axis being significantly smaller than the coefficient for the c-axis. The high temperature (200 K < T < 300 K) coefficients themselves have similar values for the compounds studied. The sharp anomalies associated with the structural/antiferromagnetic phase transitions are clearly seen in the thermal expansion measurements. For all three pure compounds the "average" a-value increases and the c-lattice parameter decreases on warming through the transition with the smallest change in the lattice parameters observed for SrFe2As2. The data are in general agreement with the literature data from X-ray and neutron diffraction experiments

Specific heat jump at the superconducting transition temperature in Ba(Fe(1-x)Cox)2As2 and Ba(Fe(1-x)Nix)2As2 single crystals

We present detailed heat capacity measurements for Ba(Fe(1-x)Cox)2As2 and Ba(Fe(1-x)Nix)2As2 single crystals in the vicinity of the superconducting transitions. The specific heat jump at the superconducting transition temperature (Tc), Delta Cp/Tc, changes by a factor ~ 10 across these series. The Delta Cp/T$ vs. Tc data of this work (together with the literature data for Ba(Fe0.939Co0.061)2As2, (Ba0.55K0.45)Fe2As2, and (Ba0.6K0.4)Fe2As2) scale well to a single log-log plot over two orders of magnitude in Delta Cp/Tc and over about an order of magnitude in Tc, giving Delta Cp/Tc ~ Tc^2