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.

Virial expansion for a polymer chain: the two parameter approximation

1979 ◽  
Vol 367 (1729) ◽  
pp. 143-174 ◽  
Keyword(s):  
Gaussian Model ◽  
Dominant Term ◽  
Cubic Lattices ◽  
Functional Relations ◽  
Ladder Graph ◽  
Simple Rules ◽  
The Mean ◽  
Parameter Approximation ◽  
Ladder Graphs ◽  
Two Parameter

A complete diagrammatic expansion is developed for the Domb-Joyce model of an N -step chain, with an interaction w which varies between 0 and 1. Simple rules are given for obtaining the diagrams. The correspondence between these diagrams and appropriate generating functions permits computation of the coefficients of the series α 2 N ( w ) = 1 + k 1 w + k 2 w 2 + . . ., where α 2 N ( w ) is the expansion factor of the mean square end-to-end length of the chain. The dominant term in N of each of the first three k r is shown to be identical for the three cubic lattices and for the Gaussian continuum model, with the exception of a scale factor h 0 . Retention of only this dominant term yields a ‘two-parameter’ expansion equivalent to that of Zimm (1946), Fixman (1955) and others. Diagrams are classed either as ladder or as non-ladder graphs. The ladder graph contributions are summed by using functional relations of Domb & Joyce (1972). The non-ladder contributions for the first three coefficients are computed individually, thereby yielding results for k 1 , k 2 and k 3 in terms of the ‘universal’ parameter z = h 0 N 1/2 w . The terms k 1 and k 2 agree with previous computations for the Gaussian model but k 3 differs slightly.

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>

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 Standard few results on graphs difference cordial labeling and its applications

2019 ◽  
Vol 8 (9) ◽  
pp. 3247-3251
Keyword(s):  
Communication Networks ◽  
Circuit Design ◽  
Coding Theory ◽  
Research Paper ◽  
Research Article ◽  
New Ideas ◽  
The Difference

The admittance of difference cordial labelling by a graph is called a difference cordial graph. In this research paper, the difference cordial labelling behaviour of , 1 2 Pn K 1 2 Pn 2K , 2 2 Pn K corona of the book with 1 2 K ,K and 2 . K1 is examined. In this research article application part, finally we conclude that this paper will be useful in the field of coding theory, astronomy, circuit design and communication networks etc. An over view and new ideas have been proposed here.

Coding Theory

2004 ◽  
Author(s):  
San Ling ◽  
Chaoping Xing
Keyword(s):  
Coding Theory

Game Theory in Wireless and Communication Networks

2009 ◽  
Author(s):  
Zhu Han ◽  
Dusit Niyato ◽  
Walid Saad ◽  
Tamer Basar ◽  
Are Hjorungnes
Keyword(s):  
Game Theory ◽  
Communication Networks

The sense of presence in virtual environments:

2003 ◽  
Vol 15 (2) ◽  
pp. 69-71 ◽  
Author(s):  
Thomas W. Schubert
Keyword(s):  
Virtual Environments ◽  
Coding Theory ◽  
Model Building ◽  
Self Report ◽  
Survey Study ◽  
Spatial Presence ◽  
Component Structure ◽  
Sense Of Presence ◽  
Being There ◽  
Measure Sense

Abstract. The sense of presence is the feeling of being there in a virtual environment. A three-component self report scale to measure sense of presence is described, the components being sense of spatial presence, involvement, and realness. This three-component structure was developed in a survey study with players of 3D games (N = 246) and replicated in a second survey study (N = 296); studies using the scale for measuring the effects of interaction on presence provide evidence for validity. The findings are explained by the Potential Action Coding Theory of presence, which assumes that presence develops from mental model building and suppression of the real environment.

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