Related papers: An improved upper bound measure of star complexity…
Information-based complexity (IBC) is a well-defined complexity measure of any object given a description in a language and a classifier that identifies those descriptions with the object. Of course, the exact numerical value will vary…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al.…
We investigate graph based secret sharing schemes and its information ratio, also called complexity, measuring the maximal amount of information the vertices has to store. It was conjectured that in large girth graphs, where the interaction…
We consider the problem of extending the drawing of a subgraph of a given plane graph to a drawing of the entire graph using straight-line and polyline edges. We define the notion of star complexity of a polygon and show that a drawing…
In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. Precisely, we compute the norm of the vector of eigenvalues of…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
In this work, I present an optimization problem which consists of assigning entries of a stellar catalog to multiple entries of another stellar catalog such that the probability of such assignment is maximum. I show a way of modeling it as…
In this paper, we use a new method to decrease the parameterized complexity bound for finding the minimum vertex cover of connected max-degree-3 undirected graphs. The key operation of this method is reduction of the size of a particular…
A biclique of a graph $G$ is an induced complete bipartite subgraph of $G$ such that neither part is empty. A star is a biclique of $G$ such that one part has exactly one vertex. The star graph of $G$ is the intersection graph of the…
We establish a hierarchy of Euclidean stars according to their degree of complexity, as measured by the complexity factor and the complexity of the pattern of evolution. We consider both, nondissipative and dissipative systems. Solutions…
In this work, we propose a novel centrality metric, referred to as star centrality, which incorporates information from the closed neighborhood of a node, rather than solely from the node itself, when calculating its topological importance.…
The sensitivity conjecture which claims that the sensitivity complexity is polynomially related to block sensitivity complexity, is one of the most important and challenging problem in decision tree complexity theory. Despite of a lot of…
The complexity of highly interconnected systems is rooted in the interwoven architecture defined by its connectivity structure. In this paper, we develop matrix energy of the underlying connectivity structure as a measure of topological…
The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we…
Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a…
Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
By definition, a rigid graph in $\mathbb{R}^d$ (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system.…
We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a…