The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

bubble columns are gas- liquid contactors that are widely used in chemical and bio- chemical industries. high mixing that result in high heat and mass transfer rates are amongst their advantages. heat transfer in a bubble column having a bundle of heaters investigated and the variation of heat transfer coefficient with variation in heaters pitch to diameter ratios in a bundle of heaters reporte...

construction of forest roads disorders the natural trend of water movement. it is vital to make ditch and cross line drainage culvert to prevent the area from being destroyed and conduct the water of streems and vallies. determination of culvert diameters depends on the information of area discharge, physiographic characteristic, vegetation cover and site land use. in order to determine the amo...