The investigation of the asymptotic behaviour of various parameters of powers of a fixed graph leads to many fascinating problems, some of which are motivated by questions in information theory, communication complexity, geometry and Ramsey theory. In this survey we discuss these problems and describe the techniques used in their study which combine combinatorial, geometric, probabilistic and l...

In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P k n is a divisor graph if and only if n ≤ 2k + 2, where P k n is the k power of the path Pn. For powers of cycles we show that C n is a divisor graph when n ≤ 2k + 2, but is not a divisor graph when n ≥ 2k + bk2 c+ 3, where C k n is the k th power of the cycle Cn. Moreover, for odd n with 2k + 2 < n < 2k + bk2 c...

In 1988, Golumbic and Hammer characterized powers of cycles, relating them to circular-arc graphs. We extend their results and propose several further structural characterizations for both powers of cycles and powers of paths. The characterizations lead to linear-time recognition algorithms of these classes of graphs. Furthermore, as a generalization of powers of cycles, powers of paths, and ev...

In modern Russia Peter the Great, according to representative opinion polls, is considered be best figure in entire history of country, significantly outstripping popularity even domestic politicians 20th-21st centuries. This very high “folk” reputation significantlycontradicts views social scientists who see I not so much a successful national reformer, “revolutionary on throne”, but despot un...

in a world, where globalization and industrial and technological progress are the most frequently heard voices, the persian gulf yet remains as an outstanding region for the most precious strategic reserves of the world. the persian gulf  harbors as the biggest reserves of the world are a major center for the production of oil and natural gas of the world. such an importance has turned the pers...

It is shown, in particular, that L p-realizations of general elliptic systems on Rn or on compact manifolds without boundaries possess bounded imaginary powers, provided rather mild regularity conditions are satisfied. In addition, there are given some new perturbation theorems for operators possessing a bounded H00-calculus. 0. Introduction. It is the main purpose of this paper to prove under ...