ON THE SOLVABILITY OF THE NULLATOR-NORATOR PAIRS NETWORK

The paper deals with the unique solvability of a nullator-norator pairs network consisting of RLC elements and source generators. After defining the kernel of a network the normaL inverse normal, distinguished and reactance trees of the network graph are introduced. Setting out from [6] necessary and sufficient conditions are given for the unique solvability. A topological formula is introduced from which many sufficient conditions of the unique solvability can be obtained as algebraic equations between the parameters of the RLC network elements. The results of the paper are illustrated by examples. Finally. a block scheme is presented for the examination of the unique solvability by computer technique

Shape Measures of Random Increasing k

International audienceRandom increasing k-trees represent an interesting, useful class of strongly dependent graphs that have been studied widely, including being used recently as models for complex networks. We study in this paper an informative notion called connectivity-profile and derive, by several analytic means, asymptotic estimates for its expected value, together with the limiting distribution in certain cases; some interesting consequences predicting more precisely the shapes of random k-trees are also given. Our methods of proof rely essentially on a bijection between k-trees and ordinary trees, and the resolution of a linear system