Related papers: Visibility Polynomial of Some Graph Classes
We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical…
The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
The variety of mutual-visibility problems contains four members, as does the variety of general position problems. The basic problem is to determine the cardinality of the largest such sets. In this paper, these eight invariants are…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…
B$_0$-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B$_0$-VPG permutation graphs. We respond here by…
The ring of graph invariants is spanned by the basic graph invariants which calculate the number of subgraphs isomorphic to a given graph in other graphs. These subgraphs counting invariants are not algebraically independent. In our view…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…
Distinctive power of the alliance polynomial has been studied in previous works, for instance, it has been proved that the empty, path, cycle, complete, complete without one edge and star graphs are characterized by its alliance polynomial.…
The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. Effective visualization of such graphs can lead to key…
In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…
Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower…