Graph transformations are a powerful notation formally describing different aspects of modeled systems. Multiagent systems introduce distribution, parallelism and autonomous decision properties. In the paper a basic properties of the GRADIS agent’s framework, joining of both approaches, are discussed. This framework supports splitting the graph, describing a problem, onto a few partial graphs, ...

The odd edge connectivity of a graph G, denoted by o(G), is the size of a smallest odd edge cut of the graph. Let S be any given surface and be a positive real number. We proved that there is a function fS( ) (depends on the surface S and lim !0 fS( )1⁄41) such that any graph G embedded in S with the odd-edge connectivity at least fS( ) admits a nowhere-zero circular (2þ )-flow. Another major r...

The valence-band electronic structure of a clean Ni(111) surface is investigated by spin-resolved photoemission. At room temperature the orientation of the photoelectron spins on the Bloch sphere and the exchange splitting of surface and bulk states along the surface normal (Γ̅ ) are determined. All investigated states are found to have a sizable exchange splitting >50 meV. Since the splitting i...

We show that a stably ergodic diffeomorphism can be C approximated by a diffeomorphism having stably non-zero Lyapunov exponents. Two central notions in Dynamical Systems are ergodicity and hyperbolicity. In many works showing that certain systems are ergodic, some kind of hyperbolicity (e.g. uniform, non-uniform or partial) is a main ingredient in the proof. In this note the converse direction...

A splitting of an additive Abelian group G is a pair (M; S), where M is a set of integers and S is a subset of G such that every nonzero element g 2 G can be uniquely written as m h for some m 2 M and h 2 S. Splittings of groups by the set M = ff1; : : :; kg are intimately related to tilings of the n{ dimensional Euclidean space. Further, such a splitting corresponds to a perfect shift code use...

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...

We consider the following network design problem, that we call the Generalized Terminal Backup Problem: given a graph (or a hypergraph) G0 = (V,E0), a set of (at least 2) terminals T ⊆ V and a requirement r(t) for every t ∈ T , nd a multigraph G = (V,E) such that λG0+G(t, T − t) ≥ r(t) for any t ∈ T . In theminimum cost version the objective is to nd G minimizing the total cost c(E) = ∑ uv∈E c(...

In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $...

recently, e. m'{a}v{c}ajov'{a} and m. v{s}koviera proved that every bidirected eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. this result shows the validity of bouchet's nowhere zero conjecture for eulerian bidirected graphs. in this paper we prove the same theorem in a different terminology and with a short and simple proof. more precisely, we p...