Labeling Of Graph Research Articles

Heptagonal graceful labeling of caterpillar and path related graphs

Heptagonal graceful labeling of caterpillar and path related graphs

Distance antimagic labeling of circulant graphs

A distance antimagic labeling of graph $ G = (V, E) $ of order $ n $ is a bijection $ f:V(G)\rightarrow \{1, 2, \ldots, n\} $ with the property that any two distinct vertices $ x $ and $ y $ satisfy $ \omega(x)\ne\omega(y) $, where $ \omega(x) $ denotes the open neighborhood sum $ \sum_{a\in N(x)}f(a) $ of a vertex $ x $. In 2013, Kamatchi and Arumugam conjectured that a graph admits a distance antimagic labeling if and only if it contains no two vertices with the same open neighborhood. A circulant graph $ C(n; S) $ is a Cayley graph with order $ n $ and generating set $ S $, whose adjacency matrix is circulant. This paper provides partial evidence for the conjecture above by presenting distance antimagic labeling for some circulant graphs. In particular, we completely characterized distance antimagic circulant graphs with one generator and distance antimagic circulant graphs $ C(n; \{1, k\}) $ with odd $ n $.

Radial radio mean labelling of Grotzsch graph and some graphs

Radial radio mean labelling of Grotzsch graph and some graphs

Structure Seer – a machine learning model for chemical structure elucidation from node labelling of a molecular graph

We introduce a graph convolution based machine-learning model which provides a quantitative probabilistic prediction on the atom connectivity based on the composition of the molecule along with a list of atom-attributed isotropic shielding constants.

Square difference labeling and co-secure domination in middle graph of certain graphs

Square difference labeling and co-secure domination in middle graph of certain graphs

On k-super graceful graphs with extremal maximum vertex degree

Let (,)GVE be a simple and loopless graph with ||V vertices and ||E edges. For 1,k≥ a graph G is called k-super graceful if there is a bijective labeling :fVE∪→{|ikik≤≤+||V+||E−1} with ()fvu=|()()|fvfu− for every edge .vuE∈ In this paper, we study the existence of k-super graceful labeling of certain graphs with extremal maximum vertex degree.

SP Mean Difference Labeling for some Special Graphs

SP Mean Difference Labeling for some Special Graphs

From Cluster Assumption to Graph Convolution: Graph-Based Semi-Supervised Learning Revisited.

Graph-based semi-supervised learning (GSSL) has long been a research focus. Traditional methods are generally shallow learners, based on the cluster assumption. Recently, graph convolutional networks (GCNs) have become the predominant techniques for their promising performance. However, a critical question remains largely unanswered: why do deep GCNs encounter the oversmoothing problem, while traditional shallow GSSL methods do not, despite both progressing through the graph in a similar iterative manner? In this article, we theoretically discuss the relationship between these two types of methods in a unified optimization framework. One of the most intriguing findings is that, unlike traditional ones, typical GCNs may not effectively incorporate both graph structure and label information at each layer. Motivated by this, we propose three simple but powerful graph convolution methods. The first, optimized simple graph convolution (), is a supervised method, which guides the graph convolution process with labels. The others are two "no-learning" unsupervised methods: graph structure preserving graph convolution () and its multiscale version GGCM, both aiming to preserve the graph structure information during the convolution process. Finally, we conduct extensive experiments to show the effectiveness of our methods.

Robust Label Propagation and Graph Embedding for Cross-Domain Image Classification

Robust Label Propagation and Graph Embedding for Cross-Domain Image Classification

Radio number of $ 2- $ super subdivision for path related graphs

<abstract><p>We studied radio labelings of graphs in response to the Channel Assignment Problem (CAP). In a graph $ G, $ the radio labeling is a mapping $ \varpi:V(G) \rightarrow \{0, 1, 2, ..., \}, $ such as $ |\varpi(\mu')-\varpi(\mu'')|\geq diam(G)+1-d(\mu', \mu''). $ The label of $ \mu $ for under $ \varpi $ is defined by the integer $ \varpi(\mu), $ and the span under is defined by $ span(\varpi) = max \{|\varpi(\mu')-\varpi(\mu'')|: \mu', \mu'' \in V(G)\}. $ $ rn(G) = min_{\varpi} span(\varpi) $ is defined as the radio number of $ G $ when the minimum over all radio labeling $ \varpi $ of $ G $ is taken. $ G $ is said to be optimal if its radio labeling is $ span(\varpi) = rn(G). $ A graph H is said to be an $ m $ super subdivision if $ G $ is replaced by the complete bipartite graph $ K_{m, m} $ with $ m = 2 $ in such a way that the end vertices of the edge are merged with any two vertices of the same partite set $ X $ or $ Y $ of $ K_{m, m} $ after removal of the edge of $ G $. Up to this point, many lower and upper bounds of $ rn(G) $ have been found for several kinds of graph families. This work presents a comprehensive analysis of the radio number $ rn(G) $ for a graph $ G $, with particular emphasis on the $ m $ super subdivision of a path $ P_{n} $ with $ n (n \geq 3) $ vertices, along with a complete bipartite graph $ K_{m, m} $ consisting of $ m $ v/ertices, where $ m = 2 $.</p></abstract>

Unveiling the Potential of Similarity Measures in Rough Labeling of Graphs

Unveiling the Potential of Similarity Measures in Rough Labeling of Graphs

Lucky edge geometric mean labeling of graphs and applications in electrical networks

A Lucky Edge Geometric Mean Labeling (LEGML) is a function μ that assigns the integers to the vertices of graph G such that for every edge as ‘{E}’, uv∈E(G) there exists a function μ*:E(G) → N is defined by μ* (uv) = √μ(u)μ(v) (or) √μ(u)μ(v) with the state that μ* (uv) ≠ μ* (vw) whenever {u} and {vw} have a common vertex as {v}. A minor number ‘k→ E = {1, 2, 3 … k} is the LEGML of G and is signified by h¢GM(G). A result that accepts LEGML is the Lucky Edge Geometric Mean Graph (LEGMG). The idea of the Graph Theory (GT) concept is fused into the Electric Circuit (EC), and the related complicated problems are transformed into graph model representation problems; as a result, the valuation method is simplified and optimized. Network analysis means finding the current or voltage in each branch. One application of GT is the representation of EC. An ‘E’ in a diagram can signify anything in an EC. Each part of the diagram can represent a port or a terminal in the EC. In this article, we have to investigate the Middle Graph (MG) of the star, the Total Graph (TG) of the star, and the central graph (CG) of the star, which accepts LEGML and LEGMG. This method also computes the power consumed by all the resistors of the EC by LEGML.

δ and prime-labelling of a tree from caterpillars

This paper explores δ-labelling and prime labelling for trees derived from caterpillar structures. In δ-labelling, vertex labels induce injective edge labels, while prime labelling ensures adjacent vertices have a greatest common divisor of one. An algorithm for efficiently labelling caterpillar trees using both methods is introduced. These labelling techniques have practical applications in network security and cryptography, providing new strategies to strengthen the security and robustness of communication networks and cryptographic systems.

Cross-Spatiotemporal Graph Convolution Networks for Skeleton-Based Parkinsonian Gait MDS-UPDRS Score Estimation.

Gait impairment in Parkinson's Disease (PD) is quantitatively assessed using the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS), a well-established clinical tool. Objective and efficient PD gait assessment is crucial for developing interventions to slow or halt its advancement. Skeleton-based PD gait MDS-UPDRS score estimation has attracted increasing interest in improving diagnostic efficiency and objectivity. However, previous works ignore the important cross-spacetime dependencies between joints in PD gait. Moreover, existing PD gait skeleton datasets are very small, which is a big issue in deep learning-based gait studies. In this work, we collect a sizable PD gait skeleton dataset by multi-view Azure Kinect sensors. The collected dataset contains 102 PD patients and 30 healthy older adults. In addition, gait data from 16 young adults (aged 24-50 years) are collected to further examine the effect of age on PD gait assessment. For skeleton-based automatic PD gait analysis, we propose a novel cross-spatiotemporal graph convolution network (CST-GCN) to learn complex features of gait patterns. Specifically, a gait graph labeling strategy is designed to assemble and group cross-spacetime neighbors of the root node according to the spatiotemporal semantics of the gait skeleton. Based on this strategy, the CST-GCN module explicitly models the cross-spacetime dependencies among joints. Finally, a dual-path model is presented to realize the modeling and fusion of spatial, temporal, and cross-spacetime gait features. Extensive experiments validate the effectiveness of our method on the collected dataset.

Large-Scale Graph Label Propagation on GPUs

Large-Scale Graph Label Propagation on GPUs

Antimagic labeling in butterfly and benes networks

This paper focus on the dynamic and rapidly evolving field of Graph Labeling research. In this paper, Antimagic Labeling for Benes and Butterfly networks has been determined. The findings can be utilized to determine the Antimagic Labeling in Interconnection networks where the routing servers acting as its vertices and the connection between them acts as edges to get the best possible solution for building a network with computational power and the ability to send and receive messages over cabled or wireless communication links.

L-VSM: Label-Driven View-Specific Fusion for Multiview Multilabel Classification.

In the task of multiview multilabel (MVML) classification, each instance is represented by several heterogeneous features and associated with multiple semantic labels. Existing MVML methods mainly focus on leveraging the shared subspace to comprehensively explore multiview consensus information across different views, while it is still an open problem whether such shared subspace representation is effective to characterize all relevant labels when formulating a desired MVML model. In this article, we propose a novel label-driven view-specific fusion MVML method named L-VSM, which bypasses seeking for a shared subspace representation and instead directly encodes the feature representation of each individual view to contribute to the final multilabel classifier induction. Specifically, we first design a label-driven feature graph construction strategy and construct all instances under various feature representations into the corresponding feature graphs. Then, these view-specific feature graphs are integrated into a unified graph by linking the different feature representations within each instance. Afterward, we adopt a graph attention mechanism to aggregate and update all feature nodes on the unified graph to generate structural representations for each instance, where both intraview correlations and interview alignments are jointly encoded to discover the underlying consensuses and complementarities across different views. Moreover, to explore the widespread label correlations in multilabel learning (MLL), the transformer architecture is introduced to construct a dynamic semantic-aware label graph and accordingly generate structural semantic representations for each specific class. Finally, we derive an instance-label affinity score for each instance by averaging the affinity scores of its different feature representations with the multilabel soft margin loss. Extensive experiments on various MVML applications have verified that our proposed L-VSM has achieved superior performance against state-of-the-art methods. The codes are available at https://gengyulyu.github.io/homepage/assets/codes/LVSM.zip.

Cycles and Paths Related Vertex-Equitable Graphs

A vertex labeling ξ of a graph χ is referred to as a ‘vertex equitable labeling (VEq.)’ if the induced edge weights, obtained by umming the labels of the end vertices, satisfy the following condition: the absolute difference in the number of vertices v and u with labels ξ(v)=a and ξ(u)=b (where a, b∈Z) is approximately 1, considering a given set A that consists of the first ⌈q2⌉ non egative integers. A graph χ that admits a vertex equitable labeling (VEq.) is termed a ‘vertex equitable’ graph. In this manuscript, we have demonstrated that graphs related to cycles and paths are examples of vertex-equitable graphs.

ABSOLUTE MEAN GRACEFUL LABELING IN THE CONTEXT OF m-SPLITTING AND DEGREE SPLITTING GRAPHS

A graph G with q edges is said to be absolute mean graceful if there is a one-to-one function f from V (G) to the set {0,±1,±2,±3,...,±q} such that when each edge xy is assigned the label |f(x)−f(y)| 2 , then the resulting edge labels are distinct. In this paper, the absolute mean graceful labeling of m-splitting and degree splitting graphs of some graphs are investigated.

CONJUGATE S3-MAGIC GRAPHS

In this paper, we introduce conjugate A-magic labeling of graphs where A is a finite non-abelian group and investigate the graphs that are conjugate S3magic.