In this article, we adapt the edge-graceful graph labeling definition into block designs and define a design V , B with id="M2"> open="|" close="|" = v id="M3"> b as block-graceful if there exists bijection ...

We propose a stringy version of the old inflation scenario which does not require any slowroll inflaton potential and is based on a specific example of string compactification with warped metric. Our set-up admits the presence of anti-D3-branes in the deep infrared region of the metric and a false vacuum state with positive vacuum energy density. The latter is responsible for the accelerated pe...

We prove that if G is a 2r-regular edge graceful (p, q) graph with (r, kp) = 1 then kG is edge graceful for odd k. We also prove that for certain specific classes of 2r-regular edge graceful graphs it is possible to drop the requirement that (r, kp) = 1

The Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of best known open problems Graph Theory. conjecture has caused a great interest study gracefulness simple graphs and led to many new contributions list graceful graphs. However, it acknowledged not much about structure after 55 years.

We studied the Einstein-Brans-Dicke cosmology in detail. The difference of the evolution of the universe is significant between Einstein-Brans-Dicke cosmology and standard big-bang model during the radiation-dominated era. The power-law evolution of the scale factor is fast enough to solve the cosmological puzzles and slow enough to avoid the graceful exit problem. However, the constraints from...

String cosmology solutions are examined in a generalized phase-space including sources representing arbitrary corrections to lowest order string-dilatongravity effective action. We find a set of necessary conditions for a graceful exit transition from a dilaton-driven inflationary phase to a radiation dominated era. We show that sources allowing such a transition have to violate energy conditio...