Total Labeling Research Articles

On Tades of Disjoint Union of Some Graphs

Consider a total labeling ξ of a graph G . For every two different edges e and f of G , let w t ( e ) ≠ w t ( f ) where weight of e = x y is defined as w t ( e ) = | ξ ( e ) – ξ ( x ) – ξ ( y ) | . Then ξ is called edge irregular total absolute difference k -labeling of G . Let k be the minimum integer for which there is a graph G with edge irregular total absolute difference labeling. This k is called the total absolute difference edge irregularity strength of the graph G , denoted t a d e s ( G ) . We compute t a d e s of S C n , disjoint union of grid and zigzag graph.

Total absolute difference edge irregularity strength of Tp-tree graphs

A total labeling ξ is defined to be an edge irregular total absolute difference k-labeling of the graph G if for every two different edges e and f of G there is wt(e) 6= wt(f) where weight of an edge e = xy is defined as wt(e) = |ξ(e) − ξ(x) − ξ(y)|. The minimum k for which the graph G has an edge irregular total absolute difference labeling is called the total absolute difference edge irregularity strength of the graph G, tades(G). In this paper, we determine the total absolute difference edge irregularity strength of the precise values for Tp-tree related graphs.

On vertex in-out-antimagic total digraphs

A vertex in-out-antimagic total labeling of a directed graph (digraph) D=(V,A) with n vertices and m arcs is a bijection from the set V∪A to the set of integers {1,2,…,m+n} such that all n vertex in-weights are pairwise distinct and simultaneously all n vertex out-weights are pairwise distinct. The vertex in-weight is the sum of the vertex label and the labels of all incoming arcs and the vertex out-weight is the sum of the vertex label and the labels of all outgoing arcs.In this paper we provide a general way how to label dense digraphs and certain sparse digraphs. Further, we add constructions of the labeling for three large infinite classes of digraphs and we conjecture that all digraphs allow such a labeling.

Efficient Graph Network Using Total Magic Labeling and Its Applications

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 processes are primarily outcomes of mathematical research. Given the increasing importance of safeguarding secret information or messages from potential intruders, it is imperative to develop effective technical tools for this purpose. These intruders are often well-versed in the latest technological advancements that could breach security. To address this, our study focuses on the efficacious combinatorial technique of graph networks using efficient domination and total magic labeling. The introduction of a graph network based on total magic labeling can significantly influence the network’s performance. This research introduces a novel combinatorial method for encrypting and decrypting confidential numbers by leveraging an efficient dominant notion and labeled graph.

TOTAL PRIME LABELING OF STAR RELATED GRAPHS

In this paper we investigate that the total prime labeling of some star graphs .we also discuss the total prime labeling in the context of some graph operation namely corona product.

A comprehensive multi-domain dataset for mitotic figure detection

The prognostic value of mitotic figures in tumor tissue is well-established for many tumor types and automating this task is of high research interest. However, especially deep learning-based methods face performance deterioration in the presence of domain shifts, which may arise from different tumor types, slide preparation and digitization devices. We introduce the MIDOG++ dataset, an extension of the MIDOG 2021 and 2022 challenge datasets. We provide region of interest images from 503 histological specimens of seven different tumor types with variable morphology with in total labels for 11,937 mitotic figures: breast carcinoma, lung carcinoma, lymphosarcoma, neuroendocrine tumor, cutaneous mast cell tumor, cutaneous melanoma, and (sub)cutaneous soft tissue sarcoma. The specimens were processed in several laboratories utilizing diverse scanners. We evaluated the extent of the domain shift by using state-of-the-art approaches, observing notable differences in single-domain training. In a leave-one-domain-out setting, generalizability improved considerably. This mitotic figure dataset is the first that incorporates a wide domain shift based on different tumor types, laboratories, whole slide image scanners, and species.

Total Edge Irregularity Strength of the Cartesian Product of Bipartite Graphs and Paths

For a simple graph G = (V (G), E(G)), a total labeling ∂ is called an edge irregular total k-labeling of G if ∂ : V (G) ∪ E(G) → {1, 2, . . . , k} such that for any two different edges uv and u'v' in E(G), we have wt∂(uv) not equal to wt∂(u'v') where wt∂(uv) = ∂(u) + ∂(v) + ∂(uv). The minimum k for which G has an edge irregulartotal k-labeling is called the total edge irregularity strength, denoted by tes(G). It is known that ceil((|E(G)|+2)/3) is a lower bound for the total edge irregularity strength of a graph G. In this paper we prove that if G is a bipartite graph for which this bound is tight then this is also true for Cartesian product of G with any path.

Pelabelan Total Titik Ajaib Pada Graf Tangga

The labeling of a graph is a mapping that pairs the elements in the graph into positive integers. In this thesis, it discusses how the magic total point labeling algorithm on the ladder graph and the ladder graph and how the magic total point labeling on the ladder graph and the adder graph uses the magic square matrix modification using the durer method. Where the elements of the result of this magic square matrix modification will be used as point labels on the ladder graph and the ladder graph.

A note on vertex irregular total labeling of trees

The total vertex irregularity strength of a graph <em>G=</em>(<em>V,E</em>) is the minimum integer <em>k</em> so that there is a mapping from <em>V ∪ E</em> to the set {<em>1,2,...,k</em>} so that the vertex-weights (i.e., the sum of labels of a vertex together with the edges incident to it) are all distinct. In this note, we present a new sufficient condition for a tree to have total vertex irregularity strength ⌈(<em>n</em><sub>1</sub><em>+1</em>)<em>/2</em>⌉<em><em>, where <em>n<sub>1</sub></em> is the number of vertices of degree one in the tree.</em></em>

Local total anti-magic chromatic number of graphs

Let G=(V,E) be a graph without isolated vertices and let |V(G)|=n and |E(G)|=m. A bijection π:V(G)∪E(G)→{1,2,....,n+m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u)≠ω(v), where u and v in V(G) (ii.) for any two adjacent edges e and e′, ω(e)≠ω(e′) (iii.) for any edge uv∈E(G) is incident to the vertex v, ω(v)≠ω(uv), where weight of vertex u is, ω(u)=∑e∈S(u)π(e), S(u) is the set of edges with every edge of S(u) one end vertex is u and an edge weight is ω(e=uv)=π(u)+π(v). In this paper, we have introduced a local total anti-magic labeling (LTAL) and the local total anti-magic chromatic number (LTACN). Also, we obtain the LTACN for the graphs Pn, K1,n, Fn and Sn,n.

On the Total Irregularity Strength of the Corona Product of a Path with Path


 This paper deals with the totally irregular total labeling of the corona product of a path with path, cycle, and star. The results gave the exact values of the total irregularity strength of pm \dot Pn and for integer 2 \leq m \leq 3 and n\geq 3

TOTAL EDGE IRREGULAR LABELING FOR TRIANGULAR GRID GRAPHS AND RELATED GRAPHS

Let be a graph with and are the set of its vertices and edges, respectively. Total edge irregular -labeling on is a map from to satisfies for any two distinct edges have distinct weights. The minimum for which the satisfies the labeling is spoken as its strength of total edge irregular labeling, represented by . In this paper, we discuss the tes of triangular grid graphs, its spanning subgraphs, and Sierpiński gasket graphs.

Determining the severity of Parkinson’s disease in patients using a multi task neural network

Parkinson’s disease is easy to diagnose when it is advanced, but it is very difficult to diagnose in its early stages. Early diagnosis is essential to be able to treat the symptoms. It impacts on daily activities and reduces the quality of life of both the patients and their families and it is also the second most prevalent neurodegenerative disorder after Alzheimer in people over the age of 60. Most current studies on the prediction of Parkinson’s severity are carried out in advanced stages of the disease. In this work, the study analyzes a set of variables that can be easily extracted from voice analysis, making it a very non-intrusive technique. In this paper, a method based on different deep learning techniques is proposed with two purposes. On the one hand, to find out if a person has severe or non-severe Parkinson’s disease, and on the other hand, to determine by means of regression techniques the degree of evolution of the disease in a given patient. The UPDRS (Unified Parkinson’s Disease Rating Scale) has been used by taking into account both the motor and total labels, and the best results have been obtained using a mixed multi-layer perceptron (MLP) that classifies and regresses at the same time and the most important features of the data obtained are taken as input, using an autoencoder. A success rate of 99.15% has been achieved in the problem of predicting whether a person suffers from severe Parkinson’s disease or non-severe Parkinson’s disease. In the degree of disease involvement prediction problem case, a MSE (Mean Squared Error) of 0.15 has been obtained. Using a full deep learning pipeline for data preprocessing and classification has proven to be very promising in the field Parkinson’s outperforming the state-of-the-art proposals.

Strong vertex-magic and super edge-magic total labelings of the disjoint union of a cycle with 3-cycles

For more than half a century, the question of deciding which 2-regular graphs possess an edge-magic total labeling remains unsolved. A particularly difficult case involves those 2-regular graphs with many components isomorphic to C3, the cycle on three vertices. For 2-regular graphs, there is an obvious correspondence between an edge-magic total labeling and a vertex-magic total labeling (VMTL). The VMTL is strong or, it is a SVMTL if the smallest labels are used on the vertices. In this paper it is shown that each of the following disjoint unions has a SVMTL, and therefore a super edge-magic total labeling: for t≥4, C6∪(2t−1)C3, C8∪(2t−1)C3, C10∪(2t−1)C3 and 2C5∪(2t−1)C3; for t≥3, C9∪2tC3; for t≥2, C11∪2tC3. Combined with previous work, this now means that each disjoint union Cm∪sC3 of odd order possesses a SVMTL for each m such that 3≤m≤11, with the exception of three known graphs: C4∪C3, C5∪2C3 and C4∪3C3. This supports the conjecture stating that these are the only odd-order 2-regular graphs without a SVMTL. It also results in further evidence supporting MacDougall's conjecture regarding which regular graphs possess VMTLs, in general.It is a noteworthy feature of the proofs that a single Kotzig array is used to prove multiple theorems, providing a unifying element to labelings of different types of 2-regular graphs. The proofs are constructive, and this work is self-contained.

ON SUPER (3n+5,2)- EDGE ANTIMAGIC TOTAL LABELING AND IT’S APPLICATION TO CONSTRUCT HILL CHIPER ALGORITHM

Graph labeling can be implemented in solving problems for various fields of life. One of the application of graph labelling is in security system. Information security is needed to reduce risk, data manipulation, and unauthorized destruction or destruction of information. Cryptographic algorithms that can be used to build security systems, one of the cryptographic algorithms is Hill Cipher. Hill chipper is a cryptographic algorithm that uses a matrix as a key to perform encryption, decryption, and modulo arithmetic. This study discusses the use of Super (3n+5,2)- edge antimagic total labeling to construct the Hill Chiper algorithm. The variation of the edge weight function and the corresponding edge label on the graph, will make the constructed lock more complicated to hack

On (a,d)-total edge irregular labelings

A total edge irregular [Formula: see text]-labeling of a graph [Formula: see text], [Formula: see text] is a labeling of vertices and edges of [Formula: see text] in such a way that the weights of all edges are distinct. A total edge irregularity strength of graph [Formula: see text], denoted by [Formula: see text] is defined as the minimum [Formula: see text] for which a graph [Formula: see text] has a totally irregular total [Formula: see text]-labeling. In this paper, we define [Formula: see text]-total edge irregularity labeling and provide the irregularity strength for some well-known families of graphs.

Union Of 4-Total Prime Cordial Graph G With The Bistar Bn,N

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k ∈ N is a variable and k > 1. For each edge uv, assign the label gcd(f (u), f (v)). The map f is called a k- Total prime cordial labeling of G if |tpf (i) − tpf (j)| ≤ 1, i, j ∈
 {1, 2, · · · , k} where tpf (x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of G ∪ Bn,n, where G has a 4-total prime cordial labeling and Bn,n is a bistar.

Perfectly antimagic total graphs

An one-one correspondence function λ from V(G) ∪ E(G) to the set {1, 2, …, |V(G) | + |E(G) |} is a total labeling of a finite undirected graph G without loops and multiple edges, where |V(G) |and |E(G) | are the cardinality of vertex and edge set of G respectively. A perfectly antimagic total labeling is a totally antimagic total labeling whose vertex and edge-weights that are also pairwise distint. Perfectly antimagic total (PAT) graph is a graph having such labeling. The topic of discovering perfectly antimagic total labeling of some families of graphs is discussed in this paper. We also came up with certain conclusions about dual of a perfectly antimagic total graphs. Finally, we provided that the necessary and sufficient condition for a dual of a regular and irregular PAT graph to be a PAT graph.

On local antimagic total labeling of complete graphs amalgamation

Let \(G = (V,E)\) be a connected simple graph of order \(p\) and size \(q\). A graph \(G\) is called local antimagic (total) if \(G\) admits a local antimagic (total) labeling. A bijection \(g : E \to \{1,2,\ldots,q\}\) is called a local antimagic labeling of $ if for any two adjacent vertices \(u\) and \(v\), we have \(g^+(u) \ne g^+(v)\), where \(g^+(u) = \sum_{e\in E(u)} g(e)\), and \(E(u)\) is the set of edges incident to \(u\). Similarly, a bijection \(f:V(G)\cup E(G)\to \{1,2,\ldots,p+q\}\) is called a local antimagic total labeling of \(G\) if for any two adjacent vertices \(u\) and \(v\), we have \(w_f(u)\ne w_f(v)\), where \(w_f(u) = f(u) + \sum_{e\in E(u)} f(e)\). Thus, any local antimagic (total) labeling induces a proper vertex coloring of \(G\) if vertex \(v\) is assigned the color \(g^+(v)\) (respectively, \(w_f(u)\)). The local antimagic (total) chromatic number, denoted \(\chi_{la}(G)\) (respectively \(\chi_{lat}(G)\)), is the minimum number of induced colors taken over local antimagic (total) labeling of \(G\). In this paper, we determined \(\chi_{lat}(G)\) where \(G\) is the amalgamation ofcomplete graphs. Consequently, we also obtained the local antimagic (total) chromatic number of the disjoint union of complete graphs, and the join of \(K_1\) and amalgamation of complete graphs under various conditions. An application of local antimagic total chromatic number is also given.

On the super (a, d)-H-antimagic total labelings of three graphs

The conception of (a, d)-H-super antimagic total labeling is generated by graph covering, magic square and graph labeling. In this paper we study the (a, d)-H-super antimagic total labelings of the friendship graph Fn, wheel Wn and the graph mG.