In this paper, we have identified some of the graceful graphs which are obtained from the amalgamations of two graceful graphs. A conjecture is also discussed for general graceful graphs and the same is proved for Fibonacci graceful graphs. Mathematics Subject Classification: 05C78

7 Partial cubes are graphs that allow isometric embeddings into hypercubes. -graceful labelings of partial cubes are introduced as a natural extension of graceful labelings of trees. It is shown that several classes of partial cubes are -graceful, for instance even 9 cycles, Fibonacci cubes, and (newly introduced) lexicographic subcubes. The Cartesian product of -graceful partial cubes is again...

We present a brief review of recent advances in string cosmology. Starting with the Dilaton-Moduli Cosmology (known also as the Pre Big Bang), we go on to include the effects of axion fields and address the thorny issue of the Graceful Exit in String Cosmology. This is followed by a review of density perturbations arising in string cosmology and we finish with a brief introduction to the impact...

Let F be a 2-regular graph of order v. The Oberwolfach problem OP(F), posed in 1967 and still open, asks for decomposition Kv into copies F. In this paper we show that OP(F) has solution whenever sufficiently large cycle which meets given lower bound and, addition, single-flip automorphism, is an involutory automorphism acting as reflection on exactly one the cycles Furthermore, prove analogous...

Motivated by brane cosmology we solve the Einstein equations with a time dependent cosmological constant. Assuming that at an early epoch the vacuum energy scales as 1/logt, we show that the universe passes from a fast growing phase (inflation) to an expanding phase in a natural way.

there are many long-standing conjectures related with some labellings of trees. it is important to connect labellings that are related with conjectures. we find some connections between known labellings of simple graphs.