In this paper, we investigate the necessary and sufficient conditions under which a class of nonlinear systems are state feedback equivalent to negative imaginary (NI) with positive definite storage functions. The interest have normal form relative degree less than or equal two. nonlinearity system is restricted respect subset variables, variables that external dynamics. Under mild assumptions,...

It is known that non-isomorphic coupled cell networks can have equivalent dynamics. Such networks are said to be ODE-equivalent and are related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE-equivalence class is said to be minimal if it has a minimum number of edges. When studying a given network in an ODE-class it can be of great value to study inst...

Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAOs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many related fields. Because different ADOs may determine the same Markov equivalence class, it long has been of interest to determine the efficiency gained in model ...

An end of a graph G is an equivalence class rays, where two rays are equivalent if there infinitely many vertex-disjoint paths between them in G. The degree the maximum cardinality collection pairwise disjoint this class.

Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...