Labeling Of Graph Research Articles

Weighted cross-modal hashing with label enhancement

Hashing has been extensively studied for large-scale cross-modal retrieval. However, there are still some unexplored issues with existing methods. First, both the initially-provided similarity graph and one-hot label vector only logically describe the yes or no information, which cannot exactly reflect the correlation between instances. Second, all bits in a binary code contribute equally to Hamming distance, which limits its discriminability to preserve refined semantics. To address these limitations, this paper presents a new method, dubbed Weighted Cross-Modal Hashing (WCMH). It introduces the topological structure of categories to enhance the logical labels, i.e., to recover the real-valued distribution of categories. Moreover, we design a weighted Hamming distance that can enlarge the range of distance values by adaptively learning the weights of different hash bits. In light of this, more discriminative information is embedded into hash codes, and the enhanced semantics can be preserved as much as possible. Extensive experiments validate the superior performance of our WCMH, in comparison with some state-of-the-art cross-modal hashing approaches.

Even vertex odd mean labeling of uniform theta graphs

Let $G$ be a graph with $p$ vertices and $q$ edges. A total graph labeling $ f:V(G)\bigcup E(G)\rightarrow \{0,1,2,3,...,2q\}$ is called even vertex odd mean labeling of a graph $G$ if the vertices of the graph $G$ label by distinct even integers from the set $\{0,2,...,2q\}$ and the labels of the edges are defined as the mean of the labels of its end vertices and these labels are $2q-1$ distinct odd integers from the set $\{1,3,5,...,2q-1\}$. In this paper we investigate the even vertex odd mean labeling of uniform theta graphs.

Group vertex magic labeling of some special graphs

For any additive abelian group $A$. Let $\mu$ be an element of $A$, a graph $G=(V,E)$ is said to be $A$-vertex magic graph if there exist a labeling function $f:V(G)\rightarrow A\setminus\{0\}$ such that $\omega(v)=\sum_{u\in N(v)} f(u)=\mu$ for any vertex $v$ of $G$, where $N(v)$ is the set of the open neighborhood of $v$. In this paper, we prove that the graphs such as wheel, Corona $C_{n}\odot mk$, subdivision of ladder and $t$-fold wheel for $t\neq n$ nor $n-2$ are $A$-vertex magic graphs. Also we prove that the subdivide wheel, helm and closed helm are $Z_{k}$-vertex magic graphs. However we prove that the triangular book and $t$-fold wheel for $t=n,n-2$ are group vertex magic graphs.

A PROPERLY EVEN HARMONIOUS LABELING OF SOME WHEEL GRAPH W_n FOR n IS EVEN

A properly even harmonious labeling of a graph G with q edges is an injective mapping f from the vertices of graph G to the integers from 0 to 2q-1 such that induces a bijective mapping f* from the edges of G to {0,2,...,2q-2} defined by f*(v_iv_j)=(f(v_i)+f(v_j))(mod2q). A graph that has a properly even harmonious labeling is called a properly even harmonious graph. In this research, we will show the existence of a properly even harmonious labeling of some wheel graph W_n for n is even.

Vertex Sum Cube Labeling for Split and Mirror Graphs

In this paper, the new concept vertex sum cube labeling has been introduced and a formula for vertex sum cube labeling has been established.

KAGNN: Graph neural network with kernel alignment for heterogeneous graph learning

Current studies have proposed the incorporation of kernel methods with graph representation learning, and graph kernels have attracted widespread attention for assessing graph similarity. However, owing to graph heterogeneity, developing appropriate kernels to extract complex structures and semantics from heterogeneous graphs is challenging. In this study, we developed a kernel-based heterogeneous graph neural network (GNN) model with a novel graph label kernel and an alignment-based aggregation mechanism. The graph label kernel captures the heterogeneous characteristics and integrates them with the graph aggregation mechanism into a unified framework. We employed the kernel alignment mechanism in a GNN framework to update node representation. The developed alignment-based GNN framework can automatically process feature propagation by modeling the similarity between node pairs and aligning the similarity matrix with the label kernel. Furthermore, model training avoids complex aggregation processes and captures distinguishable features during kernel alignment. Finally, we conducted a theoretical analysis to demonstrate the effectiveness of our method. Considering practicality, we optimized the implementation to reduce the running costs. We tested our method on three typical datasets, and the results showed that it outperformed state-of-the-art baselines.

Some Results on Odd-Even Congruence Labeling of Graphs

Introduction: Labeling of graphs has been introduced in 1966. Assignment of natural numbers to vertices and/or edges is referred as graph labeling. Inspired by the ample application of graph labeling technique in real life problems, multifarious labeling strategy was adopted and investigated by many researchers.
 Objectives:Graph labeling plays a vital role in various fields and can be implemented in multitudinous discipline including coding theory, X-ray, Psychology, crystallography, circuit design, communication networks, astronomy, radar, data security, secret sharing, data base management and so on. Apart from these labeling techniques serve as a model to understand discrete mathematical domains.
 Methodology:In this paper, an attempt has been made to introduce new labeling such as odd-even congruence labeling. Congruence Graph Labeling is an allocation of natural numbers as labels for the edges and vertices of a graph based on modular arithmetic property. Odd-even congruence labeling is an allocation of odd integers to vertices and even integers to edges in addition to congruence graph labeling.
 Result: The suggested labeling has been identified on complete bipartite graph, comb graph and spliting graph of a star graph. Further, it is proved that graph acquired by connecting two copies of even cycle Cr by a path Pt, K1,t⊗P2 and D2 (Pt) are odd-even congurence graph.

On Super (a,d)-C_3- Antimagic Total Labeling of Dutch Windmill Graph D_3^m

This paper is aimed to investigate the existence of super (a,d)-C_3- antimagic total labeling of dutch windmill graph D_3^m . The methods to achieves the goal was taken in three step. First of all determine the edge and vertices notation on dutch windmill graph . At the second step, labeling the vertices and edges of several dutch windmill graphs, then obtained the pattern. Finally pattern must be proven to become theorem. Based on the study, The Dutch Windmill Graph D_3^m, with m>=2 has super (14m+9,5)-C_3- antimagic total labeling, super (13m+8,3)-C_3- antimagic total labeling, super (12m+9.,5)-C_3- antimagic total labeling, super (11m+10.,7)-C_3- antimagic total labeling, super (10m+8.,3)-C_3- antimagic total labeling.

Joint Label Propagation, Graph and Latent Subspace Estimation for Semi-supervised Classification

Joint Label Propagation, Graph and Latent Subspace Estimation for Semi-supervised Classification

Enhanced Security in Public Key Cryptography: A Novel Approach Combining Gaussian Graceful Labeling and NTRU Public Key Cryptosystem

This research explores an encryption system that combines the Nth-degree Truncated Polynomial Ring Unit (NTRU) public key cryptosystem with Gaussian Graceful Labeling. This process assigns distinct labels to a graph's vertices, resulting in successive Gaussian integers. The NTRU method offers enhanced security and efficient key exchange. The communication encryption process depends on integers P, a, and b, with P being the largest prime number in the vertex labeling. The original receivers are the vertex labeling with the largest prime number coefficient, while all other receivers receive messages from the sender. A polynomial algebraic mixing system and a clustering principle based on the abecedarian probability proposition are used in NTRU encryption and decryption. The choice of relatively prime integers p and q in NTRU plays a role in the construction of polynomial rings used for encryption and decryption, with specific choices and properties designed to ensure scheme security.

Sum labelling graphs of maximum degree two

The concept of sum labelling was introduced in 1990 by Harary. A graph is a sum graph if its vertices can be labelled by distinct positive integers in such a way that two vertices are connected by an edge if and only if the sum of their labels is the label of another vertex in the graph. It is easy to see that every sum graph has at least one isolated vertex, and every graph can be made a sum graph by adding at most n2 isolated vertices to it. The minimum number of isolated vertices that need to be added to a graph to make it a sum graph is called the sum number of the graph.The sum number of several prominent graph classes (e.g., cycles, trees, complete graphs) is already well known. We examine the effect of taking the disjoint union of graphs on the sum number. In particular, we provide a complete characterisation of the sum number of graphs of maximum degree two, since every such graph is the disjoint union of paths and cycles.

Legal Judgment Prediction via graph boosting with constraints

Legal Judgment Prediction (LJP) is a multi-task multi-label problem in the civil law system, involving the prediction of law articles, charges, and terms of penalty based on fact descriptions. However, most existing research approaches LJP as a single-label scenario, neglecting the correlations between multiple labels and failing to consider cross-task consistency constraints in a multi-label scenario. Moreover, although previous multi-task studies have proposed expert models and coarse-grained topology construction for inter-task relationships, the former neglects rich information exchange among different tasks, and the latter, if one task’s prediction is inaccurate, will affect subsequent tasks. This paper has designed legal label graphs and proposed a novel graph boosting with constraints framework, GJudge, for legal judgment prediction to address these limitations. The framework comprises a multi-perspective interactive encoder and a multi-graph attention consistency expert module. The encoder utilizes bidirectional LSTM, gated attention units, cross attention, and graph attention networks to integrate fact descriptions and label similarity relationships information from legal label graphs for multi-perspective interactive encoding. The expert module utilizes the multiple expert networks and the multi-graph attention network to differentiate between confusing labels and ensure consistent constraints across tasks, this is achieved through the fusion of label consistency constraints and confusion relationships information in the legal label graphs. Experimental results on two real-world datasets across different tasks show an improvement in F1 scores ranging from at least 0.93% to a maximum of 2.97%, illustrating the effectiveness of GJudge compared to the state-of-the-art model.

Numerical and Scientific Investigation of Some Molecular Structures Based on the Criterion of Super Classical Average Assignments

Numbering a graph is a very practical and effective technique in science and engineering. Numerous graph assignment techniques, including distance-based labeling, topological indices, and spectral graph theory, can be used to investigate molecule structures. Consider the graph G, with the injection Ω from the node set to 1,2,…,∆, where ∆ is the sum of the number of nodes and links. Assume that the induced link assignment Ω∗ is the ceiling function of the average of root square, harmonic, geometric, and arithmetic means of the vertex labels of the end vertices of each edge. If the union of range of Ω of the node set and the range of Ω of the link set is the set 1,2,…,∆, then Ω is called a super classical average assignment (SCAA). This is known as the SCAA criterion. In this study, the graphical structures corresponding to chemical structures based on the SCAA criterion are demonstrated. The graphical depiction of chemical substances was first defined and second, the union of any number of cycles Cn, the tadpole graph, the graph extracted by identifying a line of any two cycles Cm and Cn, and the graph extracted by joining any two cycles by a path are all examined in this work.

Data and Label Graph Fusion for Semi-supervised Learning: Application to Image Categorization

Data and Label Graph Fusion for Semi-supervised Learning: Application to Image Categorization

The location of high-degree vertices in weighted recursive graphs with bounded random weights

AbstractWe study the asymptotic growth rate of the labels of high-degree vertices in weighted recursive graphs (WRGs) when the weights are independent, identically distributed, almost surely bounded random variables, and as a result confirm a conjecture by Lodewijks and Ortgiese (‘The maximal degree in random recursive graphs with random weights’, preprint, 2020). WRGs are a generalisation of the random recursive tree and directed acyclic graph models, in which vertices are assigned vertex-weights and where new vertices attach to $m\in\mathbb{N}$ predecessors, each selected independently with a probability proportional to the vertex-weight of the predecessor. Prior work established the asymptotic growth rate of the maximum degree of the WRG model, and here we show that there exists a critical exponent $\mu_m$ such that the typical label size of the maximum-degree vertex equals $n^{\mu_m(1+o(1))}$ almost surely as n, the size of the graph, tends to infinity. These results extend results on the asymptotic behaviour of the location of the maximum degree, formerly only known for the random recursive tree model, to the more general weighted multigraph case of the WRG model. Moreover, for the weighted recursive tree model, that is, the WRG model with $m=1$ , we prove the joint convergence of the rescaled degree and label of high-degree vertices under additional assumptions on the vertex-weight distribution, and also extend results on the growth rate of the maximum degree obtained by Eslava, Lodewijks, and Ortgiese (Stoch. Process. Appl.158, 2023).

The Budgeted Labeled Minimum Spanning Tree Problem

In order to reduce complexity when designing multi-media communication networks, researchers often consider spanning tree problems defined on edge-labeled graphs. The earliest setting addressed in the literature aims to minimize the number of different media types, i.e., distinct labels, used in the network. Despite being extensively addressed, such a setting completely ignores edge costs. This led to the definition of more realistic versions, where budgets for the total cost, or the number of distinct labels allowed, were introduced. In this paper, we introduce and prove the NP-hardness of the Budgeted Labeled Minimum Spanning Tree problem, consisting in minimizing the cost of a spanning tree while satisfying specified budget constraints for each label type. This problem combines the challenges of cost efficiency and label diversity within a fixed budgetary framework, providing a more realistic and practical approach to network design. We provide three distinct mathematical programming formulations of the problem and design a Lagrangian approach to derive tighter lower bounds for the optimal solution of the problem. The performances of the proposed methods are assessed by conducting a series of computational experiments on a variety of randomly generated instances, which showed how the complexity of the problem increases as the size of the network, as well as the number of labels, increase and the budget restrictions are tightened.

Valued-inverse dombi fuzzy graphs

Fuzzy graphs as labeled graphs (fuzzy vertex labeling and fuzzy edge labeling) have many applications in real life such as complex networks, coding theory, medical sciences, communication networks, and management sciences. Also, triangular norms as a special class of functions, have many applications in fuzzy set theory, probability and statistics, and other areas. This paper considers the notations of an inverse fuzzy graph and triangular norms to introduce the new type of graphs as valued-inverse Dombi fuzzy graphs. The valued-inverse Dombi fuzzy graphs are a generalization of inverse fuzzy graphs and are dual to Dombi fuzzy graphs. For any given greater than or equal to one real number, we construct a type of Dombi inverse fuzzy graph and investigate some conditions such that the product and union of Dombi inverse fuzzy graphs be a Dombi inverse fuzzy graph.

Multi-label Feature selection with adaptive graph learning and label information enhancement

The high dimensionality and complexity of multi-label data make obtaining accurate label sets in practical applications difficult. Noisy data in the labels will affect the model’s classification performance. Existing methods only reconstruct logical labels into semantic labels to mitigate the effect of inherent noise and do not specifically address the noise. In order to solve this problem and eliminate the effect of noise, this paper proposes a multi-label feature selection method with adaptive graph learning and label information enhancement (AGLE). First, each label is represented as a combination of other labels using global label correlation, which can reconstruct the original label matrix to obtain the self-expression label matrix. Based on this, similar labels in two matrices can be considered reliable labels, and not similar may be noise. Therefore, constructing a predictive label matrix to weigh the learning of original and self-expression labels can enhance reliable information. Second, an adaptive graph is utilized to learn global label correlation to ensure that the self-expression label matrix can be continuously optimized. Then, the local label manifold structure is utilized to constrain the adaptive graph for more stable performance. Finally, the adaptive graph and ℓ2,1-norm are combined to guide learning the feature weight matrix. For the proposed method, an iterative algorithm based on alternating optimization is used to compute the weight matrix. Comparing experimental results with several state-of-the-art algorithms demonstrates the effectiveness of the AGLE method for the noise problem.

The connection between the magical coloring of trees

<p>Let $ f $ be a set-ordered edge-magic labeling of a graph $ G $ from $ V(G) $ and $ E(G) $ to $ [0, p-1] $ and $ [1, p-1] $, respectively; it also satisfies the following conditions: $ |f(V(G))| = p $, $ \max f(X) < \min f(Y) $, and $ f(x)+f(y)+f(xy) = C $ for each edge $ xy\in E(G) $. In this paper, we removed the restriction that the labeling of vertices could not be repeated, and presented the concept of magical colorings including edge-magic coloring, edge-difference coloring, felicitous-difference coloring, and graceful-difference coloring. We studied the magical colorings on the tree and proved the existence of four kinds of magical colorings on the tree from a set-ordered edge-magic labeling. Further, we revealed the transformation relationship between these kinds of colorings.</p>

Prime labeling of graphs constructed from wheel graph

A prime labeling of a simple undirected graph G is to assign unique integer labels from the set {1,2,...,|V(G)|} to each vertex such that any two adjacent vertices in the graph have labels that are relatively prime. Studying prime labeling in graphs can help us understand the structure and properties of graphs and prime labeling has potential applications in cryptography and network security. In this paper we investigate when some graphs that are constructed from wheels are prime graphs.