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We present some results about the number of rational points on a certain family of curves defined over a finite field. In a small number of cases the curves have more rational points than expected. Fibonacci numbers make an appearance, as…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency…
Motivated to find the answers to some of the questions that have occurred in recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special classes of grid graphs we started the investigation of spanning unions of cycles,…
We classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in…
We give combinatorial proofs of some enumeration formulas involving labelled threshold, quasi-threshold, loop-threshold and quasi-loop-threshold graphs. In each case we count by number of vertices and number of components. For threshold…
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…
The {\em disjointness graph} of a set system is a graph whose vertices are the sets, two being connected by an edge if and only if they are disjoint. It is known that the disjointness graph $G$ of any system of segments in the plane is {\em…
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
Constacyclic codes over finite fields are of theoretical importance as they are closely related to a number of areas of mathematics such as algebra, algebraic geometry, graph theory, combinatorial designs and number theory. However, the…
The visualization of any graph plays important role in various aspects, such as graph drawing software. Complex systems (like large databases or networks) that have a graph structure should be properly visualized in order to avoid…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…
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:…
A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the `usual suspects'. Our results imply…