We study random r-regular labelled graphs with n vertices. For r = 0(n ) we give the asymptotic number of them and show that they are almost all r-connected and hamiltonian. Proofs are based on the analysis of a simple algorithm for finding "almost" random regular graphs. (Diversity Libraries §

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Let t ≥ 1 be an integer. We show that it is NP-hard to determine if an r-regular graph is t-tough for any fixed integer r ≥ 3 t. We also discuss the complexity of recognizing if an r-regular graph is t-tough, for any rational t ≥ 1.

We investigate properties of r-modes characterized by regular eigenvalue problem in slowly rotating relativistic polytropes. Our numerical results suggest that discrete r-mode solutions for the regular eigenvalue problem exist only for restricted polytropic models. In particular the r-mode associated with l = m = 2, which is considered to be the most important for gravitational radiation driven...

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green&apos...

An R-module A is called GF-regular if, for each a ∈ A and r ∈ R, there exist t ∈ R and a positive integer n such that r(n)tr(n)a = r(n)a. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by M GF(A). Furthermore, the radical properties of A are investigated; we proved that if A is an R-module and K is a submodule of A, then MGF(K) = K∩M GF(A...

In this paper, we start a systematic study of the number of accepting states. For a regular language L, we define the complexity asc(L) as the minimal number of accepting states necessary to accept L by deterministic finite automata. With respect to nondeterministic automata, the corresponding measure is nasc(L). We prove that, for any non-negative integer n, there is a regular language L such ...

It is proved the following. Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. If a quadratic space (R, q : R → R) over R is isotropic over K, then there is a unimodular vector v ∈ R such that q(v) = 0. If char(R) = 2, then in the case of even n we assume that q is a non-singular space in the sense of [Kn] and...