Research on Information Process with a Computational Approach to Some Odd-Graceful Trees

2014 ◽  
Vol 1022 ◽  
pp. 207-210 ◽  
Author(s):  
Jian Min Xie ◽  
Bing Yao ◽  
Ming Yao ◽  
Xiang En Chen
Keyword(s):  
Communication Networks ◽  
Systems Engineering ◽  
Coding Theory ◽  
Computational Approach ◽  
Labeling Theory ◽  
Graph Labeling ◽  
Graph Colorings ◽  
Information Process ◽  
Engineering Theory ◽  
Olive Trees

Graph labeling theory has important applications in coding theory, communication networks, logistics and other aspects. In Operations Research or Systems Engineering Theory and Methods, one very often use graph colorings/labellings to divide large systems into subsystems. One can use colorings/labellings to distinguish vertices and edges between vertices in order to find fast algorithms to imitate some effective transmissions and communications in information networks. In this paper we present a computational approach to the odd-graceful labelings for some olive trees.

scholarly journals New classes of graphs with edge $ \; \delta- $ graceful labeling

2022 ◽  
Vol 7 (3) ◽  
pp. 3554-3589
Author(s):  
Mohamed R. Zeen El Deen ◽  
◽  
Ghada Elmahdy ◽  
Keyword(s):  
Positive Integer ◽  
Mathematical Models ◽  
Communication Networks ◽  
Data Security ◽  
Coding Theory ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Extensive Range ◽  
Fan Graph ◽  
Positive Integers

<abstract><p>Graph labeling is a source of valuable mathematical models for an extensive range of applications in technologies (communication networks, cryptography, astronomy, data security, various coding theory problems). An edge $ \; \delta - $ graceful labeling of a graph $ G $ with $ p\; $ vertices and $ q\; $ edges, for any positive integer $ \; \delta $, is a bijective $ \; f\; $ from the set of edge $ \; E(G)\; $ to the set of positive integers $ \; \{ \delta, \; 2 \delta, \; 3 \delta, \; \cdots\; , \; q\delta\; \} $ such that all the vertex labels $ \; f^{\ast} [V(G)] $, given by: $ f^{\ast}(u) = (\sum\nolimits_{uv \in E(G)} f(uv)\; )\; mod\; (\delta \; k) $, where $ k = max (p, q) $, are pairwise distinct. In this paper, we show the existence of an edge $ \; \delta- $ graceful labeling, for any positive integer $ \; \delta $, for the following graphs: the splitting graphs of the cycle, fan, and crown, the shadow graphs of the path, cycle, and fan graph, the middle graphs and the total graphs of the path, cycle, and crown. Finally, we display the existence of an edge $ \; \delta- $ graceful labeling, for the twig and snail graphs.</p></abstract>

An interdisciplinary strategy to advance systems engineering theory: The case of abstraction and elaboration

2020 ◽  
Vol 23 (6) ◽  
pp. 673-683
Author(s):  
Taylan G. Topcu ◽  
Konstantinos Triantis ◽  
Richard Malak ◽  
Paul Collopy
Keyword(s):  
Systems Engineering ◽  
Engineering Theory

Graph Colorings Applied in Scale-Free Networks

2013 ◽  
Vol 760-762 ◽  
pp. 2199-2204 ◽  
Author(s):  
Chao Yang ◽  
Bing Yao ◽  
Hong Yu Wang ◽  
Xiang'en Chen ◽  
Si Hua Yang
Keyword(s):  
Communication Networks ◽  
Information Networks ◽  
Chromatic Numbers ◽  
Graph Colorings ◽  
Graph Models ◽  
Important Method ◽  
Scale Free ◽  
Scale Free Networks ◽  
As Graph

Building up graph models to simulate scale-free networks is an important method since graphs have been used in researching scale-free networks and communication networks, such as graph colorings can be used for distinguishing objects of communication and information networks. In this paper we determine the avdtc chromatic numbers of some models related with researching networks.

scholarly journals New Perspectives on Classical Meanness of Some Ladder Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
A. M. Alanazi ◽  
G. Muhiuddin ◽  
A. R. Kannan ◽  
V. Govindan
Keyword(s):  
Communication Networks ◽  
Coding Theory ◽  
Transportation Engineering ◽  
Ladder Graph ◽  
Ladder Graphs

In this study, we investigate a new kind of mean labeling of graph. The ladder graph plays an important role in the area of communication networks, coding theory, and transportation engineering. Also, we found interesting new results corresponding to classical mean labeling for some ladder-related graphs and corona of ladder graphs with suitable examples.

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.

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.

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