Suppose that we are given two dominating sets Ds and Dt of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between Ds and Dt such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is k...

A nonempty set S ⊂ V is a defensive k-alliance in G = (V,E), k ∈ [−Δ,Δ] ∪ Z, if for every v ∈ S, dS(v) ≥ dS̄(v) + k. A defensive k-alliance S is called exact, if S is defensive k-alliance but is no defensive (k+1)-alliance in G. In this paper we study the mathematical properties of exact defensive k-alliances in graphs. In particular, we obtain several bounds for defensive k-alliance of a graph....

• General approach for the systematic verification of code generators • Seamless test case derivation (process) based on formal specification (i.e. graph transformation rule) • A method is suggested to create test input data for model and code using automated structural test • Results are suitable for making general assumptions about whether or not the code generator’s behaviour is correct Cont...

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained analytically for arbitrary masses. ——————————PACS 11.10.-z Field theory PACS 11.10.Kk Field theories in dimensions other than four PACS 11.15.Bt General properties ...