Related papers: Geometric-Arithmetic index and line graph
The Gini index is a function that attempts to measure the amount of inequality in the distribution of a finite resource throughout a population. It is commonly used in economics as a measure of inequality of income or wealth. We define a…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
A large number of graph invariants of the form $\sum_{uv \in E(G)} F(d_u,d_v)$ are studied in mathematical chemistry, where $uv$ denotes the edge of the graph $G$ connecting the vertices $u$ and $v$, and $d_u$ is the degree of the vertex…
We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…
In this paper, we define several measures induced by a finite directed graph. The study themselves is interesting ont only in the noncommutative probability point of view but also in the algebraic structure point of view, since to define…
A $k$-regular graph of girth $g$ is called edge-girth-regular graph, shortly egr-graph, if each of its edges is contained in exactly $\lambda$ distinct $g-$cycles. An egr-graph is called extremal for the triple $(k, g, \lambda)$ if has the…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…
In this article we introduce and study the intersection graph of graded ideals of graded rings. The intersection graph of $G-$graded ideals of a graded ring $(R,G)$ is a simple graph, denoted by $Gr_G(R)$, whose vertices are the nontrivial…
Nowadays, the analysis of complex phenomena modeled by graphs plays a crucial role in many real-world application domains where decisions can have a strong societal impact. However, numerous studies and papers have recently revealed that…
Graph mining algorithms have been playing a significant role in myriad fields over the years. However, despite their promising performance on various graph analytical tasks, most of these algorithms lack fairness considerations. As a…
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism. Let $G$ be a connected graph…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
An important measure of signed graphs is the line index of balance which has several applications in many fields. However, this graph-theoretic measure was underused for decades because of the inherent complexity in its computation which is…
Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing…
The sigma index in graph theory refers to a measure of the degree differences between vertices in a graph. The goal is to determine the graphs that have the maximum sigma index within certain classes of graphs. Abdo, Dimitrov, and Gutman…
In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph)…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.