Related papers: Cantor's Powerset Theorem, Graph-Theoretically
A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…
We extend the concept of graph energy, introduced by Gutman, to matrices. We give upper and lower bounds on matrix energy extending previous results for graphs. In particular, we estimate the energy of almost all graphs.
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
In this paper we proof that any cactus graph satisfies graph complement conjecture by finding a orthogonal representation of its complement in $\mathbb{R}^5$.
By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.
Courcelle's Theorem is an important result in graph theory, proving the existence of linear-time algorithms for many decision problems on graphs whose tree-width is bounded by a constant. The purpose of this text is twofold: to provide an…
This tutorial paper refers to the use of graph-theoretic concepts for analyzing brain signals. For didactic purposes it splits into two parts: theory and application. In the first part, we commence by introducing some basic elements from…
Graph covers are a way to describe continuous maps (and homeomorphisms) of a Cantor set, more generally than e.g.\ Bratteli-Vershik systems. Every continuous map on a zero-dimensional compact set can be expressed by a graph cover (e.g.\…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our…
A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of…
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
In order to make argumentation-based inference contestable, it is crucial to explain what changes can achieve a desired (instead of the contested) inference result. To this end, we introduce strength change explanations for quantitative…
We give a bound for the graph energy with given maximal degree in terms of the second and fourth moments of a graph. In the case in which the graph is $d$-regular we obtain the bound that is given in Van Dam, E. et al. (2014). through…
We produce a new, shorter construction of a minor-universal planar graph.
We demonstrate a one-dimensional magnetic system can exhibit a Cantor-type spectrum using an example of a chain graph with $\delta$ coupling at the vertices exposed to a magnetic field perpendicular to the graph plane and varying along the…
A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…
We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.
This paper summarizes our latest understanding and results about the application of the Mathematics Of Enumeration to Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Some preliminaries of permutation groups have…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…