Related papers: When Stars Control a Grammar's Work
For a graph $G$, the central graph $C(G)$ is the graph constructed from $G$ by subdividing each edge of $G$ with one vertex and also by adding an edge to every pair of non-adjacent vertices in $G$. Also for a graph $G$, let $\gamma(G)$ and…
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network…
A graph $G=(V,E)$ is defined as a star-$k$-PCG when it is possible to assign a positive real number weight $w$ to each vertex $V$, and define $k$ distinct intervals $I_1, I_2, \ldots I_k$, in such a way that there is an edge $uv$ in $E$ if…
A chord of a cycle $C$ is an edge joining two non-consecutive vertices of $C$. A cycle $C$ in a graph $G$ is chorded if the vertex set of $C$ induces at least one chord. In this paper, we prove that if $G$ is a graph with order $n\geq 6$…
For a simple graph $G$, a domination coloring of $G$ is a proper vertex coloring such that every vertex of $G$ dominates at least one color class, and every color class is dominated by at least one vertex. The domination chromatic number,…
For any graph $G$, the Grundy (or First-Fit) chromatic number of $G$, denoted by $\Gamma(G)$ (also $\chi_{_{\sf FF}}(G)$), is defined as the maximum number of colors used by the First-Fit (greedy) coloring of the vertices of $G$.…
In modelling complex systems with graph grammars (GGs), it is convenient to restrict the application of rules using attribute constraints and negative application conditions (NACs). However, having both attributes and NACs in GGs renders…
This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…
A set $D\subseteq V$ of a graph $G=(V,E)$ is called a restrained dominating set of $G$ if every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$. The \textsc{Minimum Restrained Domination} problem is to…
The degree sequence of a graph is a numerical method to characterize the properties of graphs. Generalized forms of degree sequences exist for complete graphs and complete graphs. Nikolopolus et al. characterized the number of spanning…
Architectural Design Rewriting (ADR, for short) is a rule-based formal framework for modelling the evolution of architectures of distributed systems. Rules allow ADR graphs to be refined. After equipping ADR with a simple logic, we equip…
The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index…
To appropriately select control nodes of a large-scale network system, we propose two control centralities called volumetric and average energy controllability scores. The scores are the unique solutions to convex optimization problems…
The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of…
This paper presents several conditions to determine strong sign controllability for diffusively-coupled undirected networks. The strong sign controllability is determined by the sign patterns (positive, negative, zero) of the edges. We…
Let $G$ be a simple graph. The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
A modulator of a graph G to a specified graph class H is a set of vertices whose deletion puts G into H. The cardinality of a modulator to various tractable graph classes has long been used as a structural parameter which can be exploited…
We describe the implementation of the masking Modified Condition/Decision Coverage (MC/DC) support in GCC 14, a powerful structural coverage metric with wide industry adoption for safety critical applications. By analyzing the structure of…
Compared to sequential learning models, graph-based neural networks exhibit excellent ability in capturing global information and have been used for semi-supervised learning tasks. Most Graph Convolutional Networks are designed with the…