相关论文: On the connected and weakly convex domination numb…

An independent dominating set of the simple graph $G=(V,E)$ is a vertex subset that is both dominating and independent in $G$. The independent domination polynomial of a graph $G$ is the polynomial $D_i(G,x)=\sum_{A} x^{|A|}$, summed over…

Let $G=(V,E)$ be a simple connected graph. A set of vertices $S\subseteq V$ is said to be a dominating set if for any vertex in $V\setminus S$ is adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of $G$ is the…

We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…

A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we focus on commutative quasi-thin weakly distance-regular digraphs, and classify such digraphs with valency more than 3.…

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…

Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of…

In a graph G, a vertex dominates itself and its neighbors. A subset S of V is called a dominating set in G if every vertex in V is dominated by at least one vertex in S. The domination number gamma G is the minimum cardinality of a…

We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to…

The proper commuting graph $\mathcal{C}^{**}(G)$ of a finite group $G$ is the simple graph whose vertices are the noncentral elements of $G$ and two distinct vertices are adjacent if they commute. In this paper, we study the domination…

Priebe et al. (2001) introduced the class cover catch digraphs and computed the distribution of the domination number of such digraphs for one dimensional data. In higher dimensions these calculations are extremely difficult due to the…

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left…

A weakly distance-regular digraph is 3-equivalenced if its attached association scheme is 3-equivalenced. In this paper, we classify the family of such digraphs under the assumption of the commutativity.

Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

We give an exact characterization of monotone graph classes C with bounded average degree that satisfy the following property: The domination number of every graph from C is bounded by a linear function of its 2-independence number.

A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a…

Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a "stronger" neighbor place (having two legions), a graph theoretical model called Roman…

We provide convex body domination results for the generalized vector-valued commutator of those operators that admit specific forms of convex body domination themselves. We also prove some strong type estimates and other consequences of…

In this article, we address the decay of correlations for dynamical systems that admit an induced weak Gibbs Markov map (not necessarily full branch). Our approach generalizes L.-S. Young's coupling arguments to estimate the decay of…

We consider a sub-class of the $f$-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or $\kappa$-convex divergences. We derive new and old relationships, based on convexity arguments, between…