In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set hereditary system is minimal determining (resolving) set. Further more, if exchange property holds at level of resolving sets, then, corresponding matroid. We give counter examples to disprove both her claims. Besides, prove there exist graphs having ...

BACKGROUND Although Black and Hispanic young adults in the U.S. are less likely than Whites to move out of the parental home and more likely than Whites to return, reasons for these differences have not been clearly identified. OBJECTIVE This study examines the ability of racial/ethnic disparities in life course transitions, socioeconomic resources, and family connectivity to account for raci...

A cycle C in a graph G is said to be dominating if E(G−C) = ∅. Enomoto et al. showed that if G is a 2-connected triangle-free graph with α(G) ≤ 2κ(G) − 2, then every longest cycle is dominating. But it is unknown whether the condition on the independence number is sharp. In this paper, we show that if G is a 2-connected triangle-free graph with α(G) ≤ 2κ(G) − 1, then G has a longest cycle which...

A graphG is fractional ID-[a, b]-factor-critical ifG−I includes a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if α(G) ≤ 4b(δ(G)−a+1) (a+1)2+4b , then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that the result is best possible in some sense.

The extraction of a desired speech signal from a noisy environment has become a challenging issue. In the recent years, the scientific community has particularly focused on multichannel techniques which are dealt with in this review. In fact, this study tries to classify these multichannel techniques into three main ones: Beamforming, Independent Component Analysis (ICA) and Time Frequency (T-F...

The Maximum Independent Set problem often arises in the following form: given n tasks which compete for the same resources, compute the largest set of tasks which can be performed at the same time without sharing resources. More generally, in case the tasks have weights (priorities), one may ask for the set of tasks of largest total weight which can be performed at the same time. This is called...

Let n(G) and α(G) be the order and the independence number of a graph G, repsectively. If G is bipartite graph, then it is well-known and easy to see that α(G) ≥ n(G) 2 . In this paper we present a constructive characterization of bipartite graphs G for which

The idea of perturbation independent decay (PID) has appeared in the context of survival-probability studies, and lately has emerged in the context of quantum irreversibility studies. In both cases the PID reflects the Lyapunov instability of the underlying semiclassical dynamics, and it can be distinguished from the Wigner-type decay that holds in the perturbative regime. The theory of the sur...