Related papers: Power domination reconfiguration
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
Recently, Haynes, Hedetniemi and Henning published the book Topics in Domination in Graphs, which comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results.…
In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph $G$, called the sub-$k$-domination number and denoted $sub_k(G)$. We show that $sub_k(G)$ is a computationally efficient sharp lower…
We present a unified analytical framework within which power control, rate allocation, routing, and congestion control for wireless networks can be optimized in a coherent and integrated manner. We consider a multi-commodity flow model with…
This paper addresses a large class of vector optimization problems in infinite-dimensional spaces with respect to two important binary relations derived from domination structures. Motivated by theoretical challenges as well as by…
The study of domination in graphs has led to a variety of domination problems studied in the literature. Most of these follow the following general framework: Given a graph $G$ and an integer $k$, decide if there is a set $S$ of $k$…
Our aim here is to address the problem of decomposing a whole network into a minimal number of ego-centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However,…
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes…
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong domination number…
In recent years, graph prompting has emerged as a promising research direction, enabling the learning of additional tokens or subgraphs appended to the original graphs without requiring retraining of pre-trained graph models across various…
We consider the problem of downlink power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To mitigate the interference among concurrent…
We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for Mycielskians of important families of graphs, and construct…
A dominating set of a graph $G=(V,E)$ is a set of vertices $D \subseteq V$ whose closed neighborhood is $V$, i.e., $N[D]=V$. We view a dominating set as a collection of tokens placed on the vertices of $D$. In the token sliding variant of…
A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or adjacent to something in the set. The domination sequence of the graph is the sequence whose $k$th term is the number…
A graph $G=(V,E)$ is called equidominating if there exists a value $t \in \mathbb{N}$ and a weight function $\omega : V \rightarrow \mathbb{N}$ such that the total weight of a subset $D\subseteq V$ is equal to $t$ if and only if $D$ is a…
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to…
Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of…
The ability of a soft robot to perform specific tasks is determined by its contact configuration, and transitioning between configurations is often necessary to reach a desired position or manipulate an object. Based on this observation, we…