Labeling Of Graph Research Articles

Uncertain Labeling Graphs and Uncertain Graph Classes (with Survey for Various Uncertain Sets)

Uncertain Labeling Graphs and Uncertain Graph Classes (with Survey for Various Uncertain Sets)

Graceful Local Antimagic Labeling of Graphs: A Pattern Analysis Using Python

Graph labeling is the process of assigning labels to vertices and edges under certain conditions. This paper investigates the graceful local antimagic labeling of various graph families, excluding symmetric labelings, using computational experiments and Python-based algorithms. Through these experiments, we identify new results and patterns within specific graph classes. The study expands on the existing literature by offering computational evidence, proposing algorithms for the verification of labelings, and exploring the relationship between the local antimagic labeling and the chromatic number. Our results increase the understanding of graph labeling and offer insights into its computational aspects.

Pair mean cordial labeling of windmill, planar grid and quasi flower snark graphs

Pair mean cordial labeling of windmill, planar grid and quasi flower snark graphs

Development of navigation systems in optimal utilization of transportation routes in topology helm graphs using graph labeling

Graph theory plays a vital role in many fields. The graph concept models many relationships and processes in physical, biological, social, transportation, and information systems. One of the essential fields in graph theory is graph labeling. Graph labeling is widely used in various applications such as coding theory, x-ray crystallography, radar, astronomy, circuit design, addressing of communication networks, database management, etc. In this research, we will examine a form of topology of transportation routes based on graph labeling. The topology of the transportation routes that will be studied is a modified of helm graph. This research aims to determine the total vertex irregularity strength of the modified helm graph denoted by Hn for n≥3. The lower bound is obtained based on the properties of the graph Hn using the existing supporting theorem. The upper bound is obtained by labeling the vertices and edges of the graph Hn in some simple cases. From this labeling, total vertex irregular labeling will be constructed for any n. Based on the results of this research, the total vertex irregularity strength of the graph Hn is

BALANCED INDEX SETS OF GRAPHS AND SEMIGRAPHS

Let G be a simple graph with vertex set V (G) and edge set E(G). Graph labeling is an assignment of integers to the vertices or the edges, or both, subject to certain conditions. For a graph G(V, E), a friendly labeling f : V (G) → {0, 1} is a binary mapping such that |vf (1) − vf (0)| ≤ 1, where vf (1) and vf (0) represents number of vertices labeled by 1 and 0 respectively. A partial edge labeling f ∗ of G is a labeling of edges such that, an edge uv ∈ E(G) is, f ∗(uv) = 0 if f (u) = f (v) = 0; f ∗(uv) = 1 if f (u) = f (v) = 1 and if f (u)̸ = f (v) then uv is not labeled by f ∗. A graph G is said to be balanced graph if it admits a vertex labeling f that satisfies the conditions, |vf (1) − vf (0)| ≤ 1 and |ef (1) − ef (0)| ≤ 1, where ef (0), ef (1) are the number of edges labeled with 0 and 1 respectively. The balanced index set of the graph G is defined as, {|ef (1) − ef (0)| : the vertex labeling f is friendly}. A semigraph is a generalization of graph. The concept of semigraph was introduced by E. Sampath Kumar. Frank Harrary has defined an edge as a 2-tuple (a, b) of vertices of a graph satisfying, two edges (a, b) and (a′, b′) are equal if and only if either a = a′ and b = b′ or a = b′ and b = a′. Using this notion, E. Sampath Kumar defined semigraph as a pair (V, X) where V is a non-empty set whose elements are called vertices of G and X is a set of n-tuples called edges of G of distinct vertices, for various n ≥ 2 satisfying the conditions: (i) Any two edges of G can have at most one vertex in common; and (ii) two edges (a1, a2, a3, ..., ap) and (b1, b2, b3, ..., bq ) are said to be equal if and only if the number of vertices in both edges must be equal, i.e p = q, and either ai = bi for 1 ≤ i ≤ p or ai = bp−i+1, 1 ≤ i ≤ p. In this article, balance index set of T (Pn), T (Wn), T (Km,n) and T (Sn) determined, and the balance index set of semigraph is introduced. Additionally, the balanced index set of semigraph Cn,m, Kn,m is determined.

Super Magic Labelling of Complete Bipartite Graphs

The study of graph labelling has focused on finding classes of graphs which admits a particular type of labelling. A graph is called super magic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. Some constructions of super magic labelling of regular graphs are described. Super magic regular complete bipartite graphs are characterized.

Farey Graceful Labeling of Graphs and Its Applications

Farey Graceful Labeling of Graphs and Its Applications

An Infinite Family of Counterexamples to a Conjecture on Distance Magic Labeling

This work is about a partition problem which is an instance of the distance magic graph labeling problem. Given positive integers n, k and p 1 ≤ p 2 ≤ ⋯ ≤ p k such that p 1 + ⋯ + p k = n and k divides ∑ i = 1 n i , we study the problem of characterizing the cases where it is possible to find a partition of the set { 1 , 2 , … , n } into k subsets of respective sizes p 1 , … , p k , such that the element sum in each subset is equal. Using a computerized search we found examples showing that the necessary condition, ∑ i = 1 p 1 + ⋯ + p j ( n − i + 1 ) ≥ j ( n + 1 2 ) / k for all j = 1 , … , k , is not generally sufficient, refuting a past conjecture. Moreover, we show that there are infinitely many such counter-examples. The question whether there is a simple characterization is left open and for all we know the corresponding decision problem might be NP-complete.

Threshold Protocol Game on Graphs with Magic Square-Generalization Labelings

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. The threshold protocol game has historically been considered using infinite, simple graphs. In general, however, players might value some relationships more than others or may have different levels of influence in the graph. These traits are described by weights on graph edges or vertices, respectively. Relative comparisons on arbitrarily weighted graphs have been studied for a variety of graphical games. Alternatively, graph labelings are functions that assign values to the edges and vertices of graphs based on a particular set of rules. This work demonstrates that the outcome of the threshold protocol game can be characterized on a magic square-generalization labeled graph. There are a variety of graph labelings that generalize the concept of magic squares. In each, the labels on similar sets of graph elements sum to a constant. The constant sums of magic square-generalization labelings mean that each player experiences a constant level of influence without needing to specify the value of players relative to one another. The game outcome is compared across different types and features of labelings.

Cyclic-coverings of Line graph L(Sn) and its Disjoint Union

A graph is a particular representation of a static network and labeling of a graph can be think of as automatic routing of data in a network topology. A visual representation of data in the form of a graph help us to look deep insight. The data science (e.g., Python Package: a computer programming language) uses graph theory concepts to study and analyze the networks. Analyzing these network is equivalent of finding a set of edges E′ for a graph G such that every vertex of G is incident with at least one edge in E′. Then E′ is called an edge-covering of G. A spanning tree of a connected graph is an example of edge-covering. A finite simple graph G is an (ad, d)-H-antimagic if the following three conditions are satisfied: G has an H-covering (H a subgraph of G), there exists a bijection α : V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G) ∪ E(G)|} and the H-weights constitute an arithmetic progression with common difference d. The above said labeling is called super if α(V ) = {1, 2, . . . , |V |}. In this research article, we focused on studying super C3-antimagic labeling of line graph of a sun-let graph for several differences and C3-supermagic labeling of its disjoint union.

Antimagic Behavior of S G p n and its Subdivision

A finite simple graph G with a subgraph H is called a super (b, d)-H-antimagic: if G has an edge covering by subgraphs H1,H2, . . . ,Ht with each Hi∼= H, i = 1, 2, . . . , t, a total labeling α such that wtαH, constitutes an arithmetic progression and α(V (G)) consists of the smallest possible integers. In this manuscript, we investigated the existence of super (b, 1)- star-antimagic labeling of Sun graphs S G p n

Rumus Umum Pelabelan L(2, 1) pada Graf Koprima Grup Bilangan Bulat Modulo m

Groups are nonempty sets equipped with binary operations and fulfill certain conditions. One example of a group is the group of integers modulo . A coprime graph of a group is a graph whose vertices are elements in and any two vertices in are directly connected if and only if the greatest common factor of the orders x and y are relatively prime. labeling has important applications in wireless telecommunication networks, where there are limited radio frequencies available and adjacent transmitters cannot use the same frequency. To overcome this problem, frequency assignment is done using the concept of labeling, where transmitters are symbolized as vertices connected by edges. labeling is a graph labeling technique that assigns non-negative integer labels to graph vertices with the rule that two directly connected vertices must have a minimum label difference of two, and two vertices that are two apart must have a minimum label difference of one. The purpose of this research is to find out the general formula for the labeling on the coprime graph of the group of integers modulo and the general formula for the minimum value of the largest label of the labeling. The steps taken in this research are to determine the coprime graph form of the group of integers modulo . Then label each vertex with a non-negative label. Then label each vertex with labeling rule. From the result of this research, it can be concluded that the coprime graph of integer group modulo has a labeling with .

Solving the minimum labeling global cut problem by mathematical programming

AbstractAn edge‐labeled graph (ELG) is a graph such that is the set of vertices, is the set of edges, is the set of labels (colors), and each edge has a label associated. Given an ELG , the goal of the minimum labeling global cut problem (MLGCP) is to find a subset such that the removal of all edges with labels in disconnects and is minimum. This work proposes three new mathematical formulations for the MLGCP, namely PART, VC, and TE as well as branch‐and‐cut algorithms to solve them. Additionally, a theoretical study was carried out on the MLGCP input graph, leading to the concept of chromatic closure, used in preprocessing algorithms for this model PART. Finally, a comprehensive polyhedral investigation of the model is performed. The computational experiments showed that the model, adopting the chromatic closure concept and its branch‐and‐cut algorithm, can solve small to average‐sized instances in reasonable times.

Sturgeon-MKIV: Constraint-Based Level and Playthrough Generation with Graph Label Rewrite Rules

Procedurally generated game levels should be completable. The representation used for levels and game mechanics impacts the types of games for which different techniques can be applied. Previous work used a constraint solving approach to simultaneously generate levels with example playthroughs, showing they can be completed using the game's mechanics. However, that work used 2D grid-based rewrite rules. In this work, we extend previous approaches by representing levels as more general graphs, and game mechanics as rewrites on node and edge labels of subgraphs. Using this approach, graph-based levels with playthroughs are generated. We describe the approach and demonstrate its application in some games with graph-based levels.

Binary vertex labelings of graphs and digraphs

A (0; 1)-labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let g be a labeling of the edge set of a graph that is induced by a labeling f of the vertex set. If both g and f are friendly then f is said to be a cordial labeling of the graph. This concept extended to directed graphs is called (2; 3)-cordiality of digraphs. We investigate the labelings that are both cordial for a graph and (2; 3)-cordial for an orientation of it. We also consider the same problem for other known binary vertex labelings of graphs.

Lost in the shuffle: Testing power in the presence of errorful network vertex labels

Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the vertex correspondence across networks is a priori known. This assumption is often untrue, and the power of the subsequent test can degrade when there are misaligned/label-shuffled vertices across networks. This power loss due to shuffling is theoretically explored in the context of random dot product and stochastic block model networks for a pair of hypothesis tests based on Frobenius norm differences between estimated edge probability matrices or between adjacency matrices. The loss in testing power is further reinforced by numerous simulations and experiments, both in the stochastic block model and in the random dot product graph model, where the power loss across multiple recently proposed tests in the literature is considered. Lastly, the impact that shuffling can have in real-data testing is demonstrated in a pair of examples from neuroscience and from social network analysis.

Pair mean cordial labeling of udukkai, octopus, drum and fire cracker graphs

In this paper, we investigate the pair mean cordial labeling behavior of udukkai graph, octopus graph, double wheel graph, barbell graph, drum graph, vanessa graph and fire cracker graph.

SPORT: A Subgraph Perspective on Graph Classification with Label Noise

Graph neural networks (GNNs) have achieved great success recently on graph classification tasks using supervised end-to-end training. Unfortunately, extensive noisy graph labels could exist in the real world because of the complicated processes of manual graph data annotations, which may significantly degrade the performance of GNNs. Therefore, we investigate the problem of graph classification with label noise, which is demanding because of the complex graph representation learning issue and serious memorization of noisy samples. In this work, we present a novel approach called S ubgra p h Set Netw or k with Sample Selection and Consis t ency Learning (SPORT) for this problem. To release the overfitting of GNNs, SPORT proposes to characterize each graph as a set of subgraphs generated by certain predefined stratagems, which can be viewed as samples from its underlying semantic distribution in graph space. Then we develop an equivariant network to encode the subgraph set with the consideration of the symmetry group. To further release the influences of noisy examples, we leverage the predictions of subgraphs to measure the likelihood of a sample being clean or noisy, followed by effective label updating. In addition, we propose a joint loss to advance the model generalizability by introducing consistency regularization. Comprehensive experiments on a wide range of graph classification datasets demonstrate the effectiveness of our SPORT. Specifically, SPORT outperforms the most competing baseline by up to 6.4%.

Multi-view representation learning with dual-label collaborative guidance

Multi-view Representation Learning (MRL) has recently attracted widespread attention because it can integrate information from diverse data sources to achieve better performance. However, existing MRL methods still have two issues: (1) They typically perform various consistency objectives within the feature space, which might discard complementary information contained in each view. (2) Some methods only focus on handling inter-view relationships while ignoring inter-sample relationships that are also valuable for downstream tasks. To address these issues, we propose a novel Multi-view representation learning method with Dual-label Collaborative Guidance (MDCG). Specifically, we fully excavate and utilize valuable semantic and graph information hidden in multi-view data to collaboratively guide the learning process of MRL. By learning consistent semantic labels from distinct views, our method enhances intrinsic connections across views while preserving view-specific information, which contributes to learning the consistent and complementary unified representation. Moreover, we integrate similarity matrices of multiple views to construct graph labels that indicate inter-sample relationships. With the idea of self-supervised contrastive learning, graph structure information implied in graph labels is effectively captured by the unified representation, thus enhancing its discriminability. Extensive experiments on diverse real-world datasets demonstrate the effectiveness and superiority of MDCG compared with nine state-of-the-art methods. Our code will be available at https://github.com/Bin1Chen/MDCG.

ZONAL LABELING OF EDGE COMB PRODUCT OF GRAPHS

Given a plane graph $G=(V,E)$. A zonal labeling of graph $G$ is defined as an assignment of the two nonzero elements of the ring $\mathbb{Z}_3$, which are $1$ and $2$, to the vertices of $G$ such that the sum of the labels of the vertices on the border of each region of the graph is $0\in\mathbb{Z}_3$. A graph $G$ that possess such a labeling is termed as zonal graph. This paper will characterize edge comb product graphs that are zonal. The results show that $P_m\trianglerighteq_eC_n$, $C_n\trianglerighteq_e C_r$, $S_p\trianglerighteq_e C_n$, and $S_p\trianglerighteq_e F_t$ are zonal in some cases, but not in others.