Related papers: Graphs and codes produced by a new method for divi…
In this paper, we introduce a connection between two classical concepts of graph theory: \; metric dimension and distinguishing number. For a given graph $G$, let ${\rm dim}(G)$ and $D(G)$ represent its metric dimension and distinguishing…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with…
We propose a simple auto-encoder framework for molecule generation. The molecular graph is first encoded into a continuous latent representation $z$, which is then decoded back to a molecule. The encoding process is easy, but the decoding…
We propose a systematic procedure for the construction of graphs associated with binary quantum stabilizer codes. The procedure is characterized by means of the following three step process. First, the stabilizer code is realized as a…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…
Research in secure multi-party computation using a deck of playing cards, often called card-based cryptography, dates back to 1989 when Den Boer introduced the "five-card trick" to compute the logical AND function. Since then, many…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
In 2006, Bar\'at and Thomassen posed the following conjecture: for each tree $T$, there exists a natural number $k_T$ such that, if $G$ is a $k_T$-edge-connected graph and $|E(G)|$ is divisible by $|E(T)|$, then $G$ admits a decomposition…
For a graph $G$, let $\sigma_{2}(G)$ be the minimum degree sum of two non-adjacent vertices in $G$. A chord of a cycle in a graph $G$ is an edge of $G$ joining two non-consecutive vertices of the cycle. In this paper, we prove the following…
It is well known that the spectrum and the Smith normal form of a matrix can be computed in polynomial time. Thus, it is interesting to explore how good are these parameters for distinguishing graphs. This is relevant since it is related to…
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
Cryptographic approaches, such as secure multiparty computation, can be used to compute in a secure manner the function of a distributed graph without centralizing the data of each participant. However, the output of the protocol itself can…
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…
In this paper, two image encryption schemes are proposed for grayscale and color images. The two encryption schemes are based on dividing each image into blocks of different sizes. In the first scheme, the two dimension ($2$D) input image…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
Generative models for source code are an interesting structured prediction problem, requiring to reason about both hard syntactic and semantic constraints as well as about natural, likely programs. We present a novel model for this problem…
A new method is introduced for bounding the separation between the value of $-k$ and the smallest eigenvalue of a non-bipartite $k$-regular graph. The method is based on fractional decompositions of graphs. As a consequence we obtain a very…