The aim of this paper is to present some odd graceful graphs. In particular we show that an odd graceful labeling of the all subdivision of double triangular snakes ( 2 k ∆ -snake ). We also prove that the all subdivision of 2 1 m∆ -snake are odd graceful. Finally, we generalize the above two results (the all subdivision of 2 k m∆ -snake are odd graceful).

The objective of this paper is to present a new class of odd graceful graphs. In particular, we show that the linear cyclic snakes (1, k) C4snake and (2, k) C4snake are odd graceful. We prove that the linear cyclic snakes (1, k) C6snake and (2, k) C6snake are odd graceful. We also prove that the linear cyclic snakes (1, k) C8snake and (2, k) C8snake are odd graceful. We generalize the above res...

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 present several constructions for terraces for cyclic groups that are zigzag terraces, graceful terraces or both. These allow us to complete the classification of imperfect twizzler terraces, unify several previously unrelated constructions of terraces from the literature, find terraces for some non-cyclic abelian groups, and show that for any given r the Oberwolfach Problem with parameters ...