A recent generalization of Vinnicombe’s ν-gap metric accommodates linear time-varying (LTV) dynamics for a class of systems with graphs that admit normalized coprime representations. Such graph representations exist for systems generated by stabilizable and detectable LTV statespace models. In general, construction of normalized coprime representations is computationally challenging. In this pa...

Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(G) is called degree coprime G if for every v∈V-D, there exist vertex u∈D such that uv∈E(G) and (deg u,deg v)=1. The minimum cardinality the domination number denoted by γ_cp (G). non-coprime v)≠1. γ_ncp We obtain some graphs.

Graph theory can give a representation of abstract mathematical systems such as groups or rings. We have many graph representations for group, in this study we use the coprime generalized quaternion group to find numerical invariants graph, which are clique number and chromatic number. The main results obtained from is equal each case order.

Graph topologies for nonlinear operators which admit coprime factorisations are defined w.r.t. a gain function notion of stability in a general normed signal space setting. Several metrics are also defined and their relationship to the graph topologies are examined. In particular, relationships between nonlinear generalisations of the gap and graph metrics, Georgiou-type formulae and the graph ...

Graph topologies for nonlinear operators which admit coprime factorisations are defined w.r.t. a gain function notion of stability. Applications to closed loop robustness for nonlinear systems are also given.

A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occurring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1, . . . , N} has |A| 8000 log N/ log log N for sufficiently large N. The proof combines results from extremal graph theory with numbe...

Recently, Katre et al. introduced the concept of coprime index a graph. They asked to characterize graphs for which is same as clique number. In this paper, we partially solve problem. fact, prove that number and zero-divisor graph an ordered set ring Zpn coincide. Also, it proved annihilating ideal graphs, co-annihilating comaximal commutative rings can be realized specially constructed posets...