This paper deals with the computation of largest robust control invariant sets (RCISs) constrained nonlinear systems. The proposed approach is based on casting search for set as a graph theoretical problem. Specifically, general class discrete-time time-invariant systems considered. First, dynamics system approximated directed graph. Subsequently, condition invariance derived and an algorithm c...

We show that the Steinitz representations of 3-connected planar graphs are correspond, in a well described way, to Colin de Verdière matrices of such graphs.

We define two invariants on graphs that represent graph properties in depth. Among our results, we show that if G is a connected multigraph with e edges and no vertex of degree 1, and if f : G → R is integrable with ∫ G f dμG = 1, then for any 0 < r ≤ 1/e there exists a connected subset U of size r such that ∫ U f dμG = r.

We describe the deenition of the SU(3) Casson invariant and outline an argument which determines the contribution of certain types of components of the at moduli space. Two applications of these methods are detailed. The rst is a connect sum formula for the SU(3) Casson invariant 3]. The second presents a strategy for computing the SU(3) Casson invariant for certain graph manifolds.

Markov width of a graph is a graph invariant defined as the maximum degree of a Markov basis element for the corresponding graph model for binary contingency tables. We show that a graph has Markov width at most four if and only if it contains no K4 as a minor, answering a question of Develin and Sullivant. We also present a lower bound of order Ω(n2−ε) on the Markov width of Kn.

We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speed-ups in the Gram matrix computation. Finally, we test the novel kernel on a wide range of chemoinformatics tasks, from anti...

It is shown that the line graph transformation G L(G) of a graph G preserves an isomorphic copy of G as the nerve of a finite simplicial complex K which is naturally associated with the Krausz decomposition of L(G). As a consequence, the homology of K is isomorphic to that of G. This homology invariance algebraically confirms several well known graph theoretic properties of line graphs and fo...

The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game domination number of a graph is bounded by a given integer is PSPACEcomplete. This contrasts the situation of the game coloring problem whose complexity is s...

Let G = (V,E), V = {1,2, . . . ,n}, be a simple graph without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0, di = d(i). A graph G is regular if and only if d1 = d2 = · · · = dn. A graph invariant I(G) is measure of irregularity of graph G with the property I(G) = 0 if and only ifG is regular, and I(G)> 0 otherwise. In this paper we introduce some new irregularity measures.

In this paper we give a homology classification of spatial embeddings of a graph by an invariant defined by Wu.