Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes

2020 ◽  
Vol 23 ◽  
Author(s):  
Ayesha Shabbir ◽  
Muhammad Faisal Nadeem ◽  
Mohammad Ovais ◽  
Faraha Ashraf ◽  
Sumiya Nasir
Keyword(s):  
Graph Theory ◽  
Lower Bound ◽  
Coding Theory ◽  
Disjoint Union ◽  
Fullerene Molecule ◽  
Graph Labeling ◽  
Fullerene Graph ◽  
Theoretical Concepts ◽  
Large Numbers ◽  
Fullerene Graphs

Aims and Objective: A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule or simply a fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory where graph theoretical concepts used to study physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory which has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry and in many other fields. For example, in chemistry vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks. Method and Results: In terms of graphs vertices represent atoms while edges stand for bonds between atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons. Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and providing their exact values. Conclusion: The lower bound for tvs (tes) depending on the number of vertices, minimum and maximum degree of a graph exists in literature while to get different weights one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound we close the case for (3,6)-fullerene graphs.

scholarly journals Computing The Irregularity Strength of Planar Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 150 ◽  
Author(s):  
Hong Yang ◽  
Muhammad Siddiqui ◽  
Muhammad Ibrahim ◽  
Sarfraz Ahmad ◽  
Ali Ahmad
Keyword(s):  
Graph Theory ◽  
Circuit Design ◽  
Planar Graphs ◽  
Coding Theory ◽  
Vital Role ◽  
Graph Labeling ◽  
X Ray Crystallography ◽  
Radar Astronomy ◽  
Base Management ◽  
Irregularity Strength

The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we determine the exact value of the total irregularity strength of three planar graphs.

scholarly journals Tree-Antimagicness of Web Graphs and Their Disjoint Union

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Zhijun Zhang ◽  
Muhammad Awais Umar ◽  
Xiaojun Ren ◽  
Basharat Rehman Ali ◽  
Mujtaba Hussain ◽  
...  
Keyword(s):  
Graph Theory ◽  
Disjoint Union ◽  
Graph Labeling ◽  
Labeled Graph ◽  
Antimagic Labeling ◽  
Research Article ◽  
Web Graphs ◽  
Vertex Set ◽  
Edge Labeling

In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

FPGA Realization of the Reconfigurable Mesh Counting Algorithm

2021 ◽  
pp. 2150157
Author(s):  
Yosi Ben-Asher ◽  
Esti Stein ◽  
Vladislav Tartakovsky
Keyword(s):  
Lower Bound ◽  
Neural Nets ◽  
Processing Elements ◽  
Large Numbers ◽  
Unrealistic Assumption ◽  
Reconfigurable Mesh ◽  
Speed Up ◽  
Optimal Tree ◽  
Pass Transistor ◽  
Signal Switching

Pass transistor logic (PTL) is a circuit design technique wherein transistors are used as switches. The reconfigurable mesh (RM) is a model that exploits the power of PTLs signal switching, by enabling flexible bus connections in a grid of processing elements containing switches. RM algorithms have theoretical results proving that [Formula: see text] can speed up computations significantly. However, the RM assumes that the latency of broadcasting a signal through [Formula: see text] switches (bus length) is 1. This is an unrealistic assumption preventing physical realizations of the RM. We propose the restricted-RM (RRM) wherein the bus lengths are restricted to [Formula: see text], [Formula: see text]. We show that counting the number of 1-bits in an input of [Formula: see text] bits can be done in [Formula: see text] steps for [Formula: see text] by an [Formula: see text] RRM. An almost matching lower bound is presented, using a technique which adds to the few existing lower-bound techniques in this area. Finally, the algorithm was directly coded over an FPGA, outperforming an optimal tree of adders. This work presents an alternative way of counting, which is fundamental for summing, beating regular Boolean circuits for large numbers, where summing a vast amount of numbers is the basis of any accelerator in embedded systems such as neural-nets and streaming. a

scholarly journals Hamming Codes: Error Reducing Techniques

2021 ◽  
Vol 9 (11) ◽  
pp. 1972-1974
Author(s):  
Rohitkumar R Upadhyay
Keyword(s):  
Lower Bound ◽  
Error Correction ◽  
Coding Theory ◽  
Hamming Distance ◽  
Error Reduction ◽  
Error Correcting Codes ◽  
Significant Other ◽  
Hamming Codes ◽  
Decoding Algorithms ◽  
Reducing Properties

Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and explored. We show a sort of lower bound on the definitely average number of errors present in a decoded message when two errors for the most part are introduced by the channel for for all intents and purposes general Hamming codes, which actually is quite significant. Other decoding algorithms are investigated experimentally, and it generally is definitely found that these algorithms for the most part improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of for all intents and purposes standard decoding. Keywords: coding theory, hamming codes, hamming distance

scholarly journals A Computational Perspective on Network Coding

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Qin Guo ◽  
Mingxing Luo ◽  
Lixiang Li ◽  
Yixian Yang
Keyword(s):  
Graph Theory ◽  
Computational Complexity ◽  
Lower Bound ◽  
Network Coding ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Multicast Networks ◽  
Computational Perspective ◽  
Source Rate

From the perspectives of graph theory and combinatorics theory we obtain some new upper bounds on the number of encoding nodes, which can characterize the coding complexity of the network coding, both in feasible acyclic and cyclic multicast networks. In contrast to previous work, during our analysis we first investigate the simple multicast network with source rateh=2, and thenh≥2. We find that for feasible acyclic multicast networks our upper bound is exactly the lower bound given by M. Langberg et al. in 2006. So the gap between their lower and upper bounds for feasible acyclic multicast networks does not exist. Based on the new upper bound, we improve the computational complexity given by M. Langberg et al. in 2009. Moreover, these results further support the feasibility of signatures for network coding.

scholarly journals Graph Theory in the Analysis of Arithmophobia

2019 ◽  
Vol 8 (12) ◽  
pp. 3637-3640
Keyword(s):  
Graph Theory ◽  
Graphical Interface ◽  
Theoretical Concepts ◽  
Wheel Graph ◽  
Student’S Performance

In this paper, Graph theoretical concepts are applied to analyze the reasons behind Arithmophobia commonly found among the students.Bull graph is used to epitomize Mild Arithmophobia which occurs when the preparation of students to face any test is deficient.Flower graph is used to represent Intense Arithmophobia. Wheel graph is used to depict the factors which desensitize Arithmophobia. Inferring information from these types of graphs is much more easier than inferring from a self map. This analysis will help in treating Arithmophobia and improve the student’s performance in Mathematics progressively. The benefits of using interactive graphical interface, graphs and graph theory metrics for a client centered analysis is also discussed

scholarly journals Super cyclic antimagic covering for some families of graphs

2021 ◽  
Vol 5 (1) ◽  
pp. 27-33
Author(s):  
Muhammad Numan ◽  
◽  
Saad Ihsan Butt ◽  
Amir Taimur ◽  
◽  
...  
Keyword(s):  
Coding Theory ◽  
Necessary Conditions ◽  
Graph Labeling ◽  
Computer Networking ◽  
Wheel Graph ◽  
Scheme Theory

Graph labeling plays an important role in different branches of sciences. It gives useable information in the study of radar, missile and rocket theory. In scheme theory, coding theory and computer networking graph labeling is widely employed. In the present paper, we find necessary conditions for the octagonal planner map and multiple wheel graph to be super cyclic antimagic cover and then discuss their super cyclic antimagic covering.

scholarly journals Chronumental: time tree estimation from very large phylogenies

2021 ◽  
Author(s):  
Theo Sanderson
Keyword(s):  
Lower Bound ◽  
Probabilistic Model ◽  
Gradient Descent ◽  
Phylogenetic Trees ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Large Numbers ◽  
Tree Estimation ◽  
Made In

Phylogenetic trees are an important tool for interpreting sequenced genomes, and their interrelationships. Estimating the date associated with each node of such a phylogeny creates a "time tree", which can be especially useful for visualising and analysing evolution of organisms such as viruses. Several tools have been developed for time-tree estimation, but the sequencing explosion in response to the SARS-CoV-2 pandemic has created phylogenies so large as to prevent the application of these previous approaches to full datasets. Here we introduce Chronumental, a tool that can rapidly infer time trees from phylogenies featuring large numbers of nodes. Chronumental uses stochastic gradient descent to identify lengths of time for tree branches which maximise the evidence lower bound under a probabilistic model, implemented in a framework which can be compiled into XLA for rapid computation. We show that Chronumental scales to phylogenies featuring millions of nodes, with chronological predictions made in minutes, and is able to accurately predict the dates of nodes for which it is not provided with metadata.

scholarly journals Graceful Labeling of Hypertrees

2021 ◽  
Vol 13 (1) ◽  
pp. 28
Author(s):  
H. El-Zohny ◽  
S. Radwan ◽  
S.I. Abo El-Fotooh ◽  
Z. Mohammed
Keyword(s):  
Graph Theory ◽  
Simple Graph ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Edge Labeling

Graph labeling is considered as one of the most interesting areas in graph theory. A labeling for a simple graph G (numbering or valuation), is an association of non -negative integers to vertices of G  (vertex labeling) or to edges of G  (edge labeling) or both of them. In this paper we study the graceful labeling for the k- uniform hypertree and define a condition for the corresponding tree to be graceful. A k- uniform hypertree is graceful if the minimum difference of vertices’ labels of each edge is distinct and each one is the label of the corresponding edge.

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