Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation...
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 is a connection of objects. These objects are often known as vertices or nodes and the connection or relation in these nodes are called arcs or edges. There are certain rules to allocate values to these vertices and edges. This allocation of...
Graphical games describe strategic interactions among a specified network of players. The threshold protocol game is a graphical game that models the adoption of a lesser-used product in a population when individuals benefit by using the same product...
A graph, G=(V,E), is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection g:E(G)→{1,3,…,2m−1}, from which an injective transformation is derived, g*:V(G)→{1,2,3,…,2m&minus...
This paper presents a general recursive formula to estimate the number of labeled graphs as well as details to evaluate the formula for the following graph properties: number of edges (graph density), degree sequence, degree distribution, classificat...
In multi-label data, a sample is associated with multiple labels at the same time, and the computational complexity is manifested in the high-dimensional feature space as well as the interdependence and unbalanced distribution of labels, which leads...
A graph’s edge labeling involves the allocation of symbols (colors or numbers) to the edges of a graph governed by specific criteria. Such labeling of a graph G with order n and size m is named edge odd graceful if there is a bijective map &phi...
Edge Even Graceful Labelingwas first defined byElsonbaty and Daoud in 2017. An edge even graceful labeling of a simple graph G with p vertices and q edges is a bijection f from the edges of the graph to the set { 2 , 4 , &...
Edge even graceful labeling (e.e.g., l.) of graphs is a modular technique of edge labeling of graphs, introduced in 2017. An e.e.g., l. of simple finite undirected graph G = ( V ( G ) , E ( G ) ) of order P = | ( V ( G ) | and siz...
In this paper, we used the permutation group together with the concept of cordiality in graph theory to introduce a new method of labeling. This construed permuted cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreover,...
The results of aerial scene classification can provide valuable information for urban planning and land monitoring. In this specific field, there are always a number of object-level semantic classes in big remote-sensing pictures. Complex label-space...
A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph G = ( V , E ) a vertex labeling is a capacity from V to an arrangement of integers. A graph...
In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph G = ( V , E ) , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a...
Recently, Multi-Graph Learning was proposed as the extension of Multi-Instance Learning and has achieved some successes. However, to the best of our knowledge, currently, there is no study working on Multi-Graph Multi-Label Learning, where each objec...
Cryptography is a pivotal application of graph theory in ensuring secure communication systems. Modern cryptography is deeply rooted in mathematical theory and computer science practices. It is widely recognized that encryption and decryption process...
Graph mining has emerged as a significant field of research with applications spanning multiple domains, including marketing, corruption analysis, business, and politics. The exploration of knowledge within graphs has garnered considerable attention...
In this paper we used the cubic roots of unit group together with the concept of cordiality in graph theory to introduce a new method of labeling, this construed cubic cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreo...
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowaday...
An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where...
The generalization of Farey graphs and extended Farey graphs all originate from Farey graphs. They are simultaneously scale-free and small-world. A labeling of the vertices for them are proposed here. All of the shortest paths between any two vertice...
In a real hyperspectral image classification task, label noise inevitably exists in training samples. To deal with label noise, current methods assume that noise obeys the Gaussian distribution, which is not the real case in practice, because in most...
Suppose that T is a plane tree without vertices of degree 2 and with at least one vertex of at least degree 3, and C is the cycle obtained by connecting the leaves of T in a cyclic order. Set G=T∪C, which is called a Halin graph. A k-L(2,1)-label...
Graph Neural Networks (GNNs) have become a cornerstone for graph classification, yet their vulnerability to backdoor attacks remains a significant security concern. While clean-label attacks provide a stealthier approach by preserving original labels...
In order to overcome the drawbacks of the ridge regression and label propagation algorithms, we propose a new semi-supervised classification method named semi-supervised ridge regression with adaptive graph-based label propagation (SSRR-AGLP). Firstl...
We study an edge irregular reflexive k-labelling for the generalized friendship graphs, also known as flowers (a symmetric collection of cycles meeting at a common vertex), and determine the exact value of the reflexive edge strength for several subf...
A labeled graph is a special structure with node identification capability, which is often used in information networks, biological networks, and other fields. The subgraph query is widely used as an important means of graph data analysis. As the siz...
Text classification is an important research field in text mining and natural language processing, gaining momentum with the growth of social networks. Despite the accuracy advancements made by deep learning models, existing graph neural network-base...
Using graphs as a data structure is a simple way to represent relationships between objects. Consequently, it has raised the need for algorithms to process, analyze, and extract meaningful information from graphs. Therefore, frequent subgraph mining...
Whole-slide histology images (WSIs) can exceed 100 k × 100 k pixels, making direct pixel-level segmentation infeasible and requiring patch-level classification as a practical alternative for downstream WSI segmentation. However, most approaches...
With the rapid advancement of the civil aviation sector and the concurrent expansion of pilot training programs, a pressing need arises for more efficient assessment methodologies during the pilot training process. Traditional written evaluations con...
Within the domain of multi-label classification for micro-videos, utilizing terrestrial datasets as a foundation, researchers have embarked on profound endeavors yielding extraordinary accomplishments. The research into multi-label classification bas...
As one of the fundamental tasks in remote sensing (RS) image understanding, multi-label remote sensing image scene classification (MLRSSC) is attracting increasing research interest. Human beings can easily perform MLRSSC by examining the visual elem...
Given n≥6, D={1,2,…,⌊n2⌋}, and a generating set S⊆D, the circulant graph Cn(S) has Zn as a vertex set in which two distinct vertices i and j are adjacent if and only if |i−j|n∈S, where |x|n=min(|x|,n−|x|)...
Molecular odor prediction represents a fundamental challenge in computational chemistry with significant applications in fragrance design, food science, and chemical safety assessment. While traditional Quantitative Structure–Activity Relations...
In order to enhance leakage detection accuracy in water distribution networks (WDNs) while reducing sensor deployment costs, an intelligent algorithm for the optimal deployment of water network monitoring sensors based on the automatic labelling and...
Multi-label arrhythmia classification from 12-lead ECG signals is a tricky problem, including spatiotemporal feature extraction, feature fusion, and class imbalance. To address these issues, a multi-scale temporal–dynamic graph convolutional wi...
Cyber-physical systems such as autonomous spacecraft, power plants and automotive systems become more vulnerable to unanticipated failures as their complexity increases. Accurate tracking of system dynamics and fault diagnosis are essential. This pap...
Indoor WLAN fingerprint localization systems have been widely applied due to the simplicity of implementation on various mobile devices, including smartphones. However, collecting received signal strength indication (RSSI) samples for the fingerprint...
A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the...
Symmetry in non-planar graphs is a fundamental concept that enhances understanding, simplifies analyses, and has practical implications in diverse fields such as science, engineering, and mathematics. A total κ-labeling for a graph Gνˇ...
Radio mean labeling of a connected graph G is an assignment of distinct positive integers to the vertices of G satisfying a mathematical constraint called radio mean condition. The maximum label assigned to any vertex of G is called the span of the r...
In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a di...
The security of traditional public key cryptography algorithms depends on the difficulty of the underlying mathematical problems. Asymmetric topological encryption is a graph-dependent encryption algorithm produced to resist attacks by quantum comput...
Annotating remote sensing images is a challenging task for its labor demanding annotation process and requirement of expert knowledge, especially when images can be annotated with multiple semantic concepts (or labels). To automatically annotate thes...
Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a...
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 integers 1,2,…,p+q, with the property that, f...
Let G=(V(G),E(G)) be a connected graph with n vertices and m edges. A bijection f:E(G)→{1,2,⋯,m} is an edge labeling of G. For any vertex x of G, we define ω(x)=∑e∈E(x)f(e) as the vertex label or weight of x, where E(x) is t...
For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G)→{1,2,…,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wtφ(v)=∑u∈N(v)φ(uv), are all different. Th...
Given a graph G with vertex set V(G) and edge set E(G), for the bijective function f(V(G))→{1,2,⋯,|V(G)|}, the associated weight of an edge xy∈E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, the function...
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