Let G be a graph class. The square root of G contains all graphs whose square belong in G. We prove that if G is non-trivial and minor closed, then all graphs in its square root have carving-width bounded by some constant depending only on G. As a consequence, every square root of such a graph class has a linear time recognition algorithm.

A simple design method is proposed for square root domain filters. The method is based on the imitation of passive filters (or their signal flow graphs). This allows square root domain topologies and parameters to be easily extracted. The method is augmented by a simple method to study and manipulate the filter’s DC point. The method is used to design a universal biquad filter as a demonstratio...

Deciding whether a given graph has a square root is a classical problem that has been studied extensively both from graph theoretic and from algorithmic perspectives. The problem is NP-complete in general, and consequently substantial effort has been dedicated to deciding whether a given graph has a square root that belongs to a particular graph class. There are both polynomial-time solvable an...

After analyzing the advantages and disadvantages of all the general algorithms adopted in designing square root on FPGA chips with pipeline technology, a proposed algorithm based on digit by digit calculation method is discussed. The algorithm is realized on the ModelSim SE 6.3f development platform with VHDL language and the simulation results show that it is characterized by occupying less re...

A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed graph classes and a very limited number of othe...