Related papers: On compositions of numbers and graphs
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
This is a collection of articles, written as sections, on arithmetic properties of differential equations, holomorphic foliations, Gauss-Manin connections and Hodge loci. Each section is independent from the others and it has its own…
Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much…
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
The adaptive processing of graph data is a long-standing research topic which has been lately consolidated as a theme of major interest in the deep learning community. The snap increase in the amount and breadth of related research has come…
This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to…
This essay recounts my personal journey towards a deeper understanding of the mathematical foundations of algorithmic music composition. I do not spend much time on specific mathematical algorithms used by composers; rather, I focus on…
In this paper I survey the sources of inspiration for my own and co-authored work in trying to develop a general theory of graph polynomials. I concentrate on meta-theorems, i.e., theorem which depend only on the form infinite classes of…
We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.
We investigate graphs that have characteristic-dependent well-covered dimension and show how more of these graphs can be constructed from known ones.
There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…
Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic…
Recently in graph theory several authors have studied the spectrum of the Cayley graph of the symmetric group S_n generated by the transpositions (1, i) for 2 <= i <= n. Several conjectures were made and partial results were obtained. The…