Related papers: A note on graphs with characteristic-dependent wel…
A constructive characterization of the class of uniformly $4$-connected graphs is presented. The characterization is based on the application of graph operations to appropriate vertex and edge sets in uniformly $4$-connected graphs, that…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective…
We study the metric dimension (strong and weak) of infinite graphs. In particular, our main interest is characterizing infinite graphs with finite dimension. Our main results: (1) graphs with more than one end have infinite strong…
A graph $G$ is well-covered if every minimal vertex cover of $G$ is minimum, and a graph $G$ is well-dominated if every minimal dominating set of $G$ is minimum. Studies on well-covered graphs were initiated in [Plummer, JCT 1970], and…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
We study the VC-dimension of the set system on the vertex set of some graph which is induced by the family of its $k$-connected subgraphs. In particular, we give tight upper and lower bounds for the VC-dimension. Moreover, we show that…
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
We study k-dependence and half domination problems for king's graphs in dimension n (n>1). Various sharp bounds are provided and a few conjectures are formulated in the cases the estimates are not the best possible.
This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.
We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of…
In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the fractional factors of graphs and the fractional…
We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
In this paper we study the main characteristics of some evaluation codes parameterized by the edges of a bipartite graph with a perfect matching.