In this paper, in the environment of Euclidean Jordan algebras, we establish some inequalities over the Krein parameters of a symmetric association scheme and of a strongly regular graph. Next, we define the modified Krein parameters of a strongly re...
This paper introduces a novel hyperspectral image super-resolution algorithm based on graph-regularized tensor ring decomposition aimed at resolving the challenges of hyperspectral image super-resolution. This algorithm seamlessly integrates graph re...
Regular two-graphs on up to 36 vertices are classified, and recently, the classification of regular two-graphs on 38 and 42 vertices having at least one descendant with a nontrivial automorphism group has been performed. The first unclassified cases...
This paper presents an alternative proof of the celebrated friendship theorem, originally established by Erdős, Rényi, and Sós in 1966. The proof relies on a closed-form expression for the Lovász ϑ-function of stron...
An antimagic labeling of a graph G=(V,E) is a bijection from the set of edges of G to 1,2,⋯,E(G) and such that any two vertices of G have distinct vertex sums where the vertex sum of a vertex v in V(G) is nothing but the sum of all the incident...
A graph containing some edges with probability measures and other edges with uncertain measures is referred to as an uncertain random graph. Numerous real-world problems in social networks and transportation networks can be boiled down to optimizatio...
We compute the Castelnuovo–Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to combine bounds on the regularity, the projective dimension, and the...
For an undirected graph G, a zero-sum flow is an assignment of nonzero integer weights to the edges such that each vertex has a zero-sum, namely the sum of all incident edge weights with each vertex is zero. This concept is an undirected analog of no...
A graph simulation and its variants are widely used in graph pattern matching. Among them, there have been related works involving the addition of regular expressions to graph patterns, which can discover more meaningful data and solve problems in po...
Let G be a connected, simple, and finite graph. For an ordered set W={w1,w2,…,wk}⊆V(G) and a vertex v of G, the representation of v with respect to W is the k-vector r(v|W)=(dG(v,w1),…,dG(v,wk)). The set W is called a resolving set...
With the growth of e-commerce platforms, the number of fraud reviews has rapidly increased, making fraud detection for platform data critically important. To detect fraud reviews in platform data, recent approaches have leveraged graph neural network...
Picture fuzzy model is a generalized structure of intuitionistic fuzzy model in the sense that it not only assigns the membership and nonmembership values in the form of orthopair ( μ , ν ) to an element, but it assigns a triplet (...
Let G=(V,E) be a finite simple graph with p=|V| vertices and q=|E| edges, without isolated vertices or isolated edges. A vertex magic total labeling is a bijection f from V∪E to the consecutive integers1,2,…,p+q, with the property that, fo...
Consensus-based data aggregation in d-regular bipartite graphs poses a challenging task for the scientific community since some of these algorithms diverge in this critical graph topology. Nevertheless, one can see a lack of scientific studies dealin...
We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach using structure coefficients defined for configurations describing such arrangeme...
In this paper, motivated by a biodegradable stent problem, we consider a parabolic differential equation on graphs. This kind of equation describes the stent material degradation in time. Since stents are mesh-like structures with thin struts, they c...
One of the main problems in the theory of strongly regular graphs (SRGs) is constructing and classifying SRGs with given parameters. Strongly regular graphs with parameters (37,18,8,9), (41,20,9,10), (45,22,10,11), (49,24,11,12), (49,18,7,6) and (50,...
Dimensionality reduction (DR) methods based on graph embedding are widely used for feature extraction. For these methods, the weighted graph plays a vital role in the process of DR because it can characterize the data’s structure information. M...
Let G be a finite simple graph on n vertices. Let J G ⊂ K [ x 1 , … , x n ] be the cover ideal of G. In this article, we obtain syzygies, Betti numbers, and Castelnuovo–Mumford regularity of J G s for all...
In recent decades, distributed consensus-based algorithms for data aggregation have been gaining in importance in wireless sensor networks since their implementation as a complementary mechanism can ensure sensor-measured values with high reliability...
In this paper, completely regular endomorphisms of unicyclic graphs are explored. Let G be a unicyclic graph and let c E n d ( G ) be the set of all completely regular endomorphisms of G. The necessary and sufficient conditions under which...
In this article, we discuss new characterizations of Cohen-Macaulay bipartite edge ideals. For arbitrary bipartite edge ideals I ( G ) , we also discuss methods to recognize regular elements on I ( G ) s for all s ≥ 1 in...
Hyperspectral unmixing, aiming to estimate the fractional abundances of pure spectral signatures in each mixed pixel, has attracted considerable attention in analyzing hyperspectral images. Plenty of sparse unmixing methods have been proposed in the...
We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = ⟨ a , b | a n = b 4 = 1 , b − 1 a b = a − 1 ⟩ , some of which generalize those ea...
Current depth map sensing technologies capture depth maps at low spatial resolution, rendering serious problems in various applications. In this paper, we propose a single depth map super-resolution method that combines the advantages of model-based...
Graph regularized non-negative matrix factorization (GNMF) is widely used in feature extraction. In the process of dimensionality reduction, GNMF can retain the internal manifold structure of data by adding a regularizer to non-negative matrix factor...
In a hyperspectral image, there is a close correlation between spectra and a certain degree of correlation in the pixel space. However, most existing low-rank representation (LRR) methods struggle to utilize these two characteristics simultaneously t...
Due to the great benefit of rich spectral information, hyperspectral images (HSIs) have been successfully applied in many fields. However, some problems of concern also limit their further applications, such as high dimension and expensive labeling....
NONNEGATIVE matrix factorization (NMF) is an effective technique for dimensionality reduction of high-dimensional data for tasks such as machine learning and data visualization. However, for practical clustering tasks, traditional NMF ignores the man...
The vertex quadrangulation QG of a 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares. In a previous work [JOMC 59, 1551–1569 (2021)],...
In the competitive landscape of online learning, developing robust and effective learning resource recommendation systems is paramount, yet the field faces challenges due to high-dimensional, sparse matrices and intricate user–resource interact...
Small target detection is a critical step in remotely infrared searching and guiding applications. However, previously proposed algorithms would exhibit performance deterioration in the presence of complex background. It is attributed to two main rea...
Cancer genomic data contain views from different sources that provide complementary information about genetic activity. This provides a new way for cancer research. Feature selection and multi-view clustering are hot topics in bioinformatics, and the...
Dimensionality reduction has always been a major problem for handling huge dimensionality datasets. Due to the utilization of labeled data, supervised dimensionality reduction methods such as Linear Discriminant Analysis tend achieve better classific...
Non-negative matrix factorization (NMF) is widely used as a powerful matrix factorization tool in data representation. However, the traditional NMF, measured by Euclidean distance or Kullback–Leibler distance, does not take into account the int...
The spectral mismatch between a multispectral (MS) image and its corresponding panchromatic (PAN) image affects the pansharpening quality, especially for WorldView-2 data. To handle this problem, a pansharpening method based on graph regularized spar...
Non-negative Matrix Factorization (NMF) has gained popularity due to its effectiveness in clustering and feature selection tasks. It is particularly valuable for managing high-dimensional data by reducing dimensionality and providing meaningful seman...
This paper provides new observations on the Lovász θ-function of graphs. These include a simple closed-form expression of that function for all strongly regular graphs, together with upper and lower bounds on that function for all regula...
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in the Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular graphs of...
Let Γ be a graph and G⩽Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p:Γ¯→Γ is arc-transitive (AT) if an AT subgroup of Aut(&...
Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of...
In this research article, we present a novel framework for handling intuitionistic fuzzy soft information by combining the theory of intuitionistic fuzzy soft sets with graphs. We introduce the notion of certain types of intuitionistic fuzzy soft gra...
A complex Pythagorean fuzzy set (CPFS) is an extension of a Pythagorean fuzzy set that is used to handle the vagueness with the degrees whose ranges are enlarged from real to complex subset with unit disc. In this research study, we propose the innov...
As an analogous concept of a nowhere-zero flow for directed graphs, zero-sum flows and constant-sum flows are defined and studied in the literature. For an undirected graph, a zero-sum flow (constant-sum flow resp.) is an assignment of nonzero intege...
In this paper, we study self-dual and LCD codes constructed from Kneser graphs K(n, 2) and collinearity graphs of generalized quadrangles using the so-called pure and bordered construction. We determine conditions under which these codes are self-dua...
The total graph of G, T(G) is the graph whose vertex set is the union of the sets of vertices and edges of G, where two vertices are adjacent if and only if they stand for either incident or adjacent elements in G. For k≥2, the k-th iterated total...
We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I(G) of a graph G, the induced matching number of G is an upper bound for the v-number of I(G) when G is very well-cov...
We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 1...
Over the past few years, there has been a surge in research attention towards tasks involving graph data, largely due to the impressive performance demonstrated by graph neural networks (GNNs) in handling such information. Currently, out-of-distribut...
Nonnegative matrix factorization (NMF) is an efficient method for feature learning in the field of machine learning and data mining. To investigate the nonlinear characteristics of datasets, kernel-method-based NMF (KNMF) and its graph-regularized ex...
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