Edge Even Graceful Labeling of Polar Grid Graphs

Daoud, S. N.

doi:10.3390/sym11010038

Cited by 9 publications

(6 citation statements)

References 9 publications

(10 reference statements)

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“…Definition 2.1. [5] The polar grid graph P m,n is the graph consists of n copies of circles C m which will be numbered from the inner most circle to the outer circle as…”

Section: Resultsmentioning

confidence: 99%

Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph

Gayathri,

Saravanakumar

2024

Proyecciones (Antofagasta)

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An k-edge-weighting of a graph G=(V,E) is a map φ: E(G) → {1, 2, 3, ..., k} where k ≥ 1 is an integer. Denote Sφ(v) is the sum of edge-weights appearing on the edges incident at the vertex v under φ. An k-edge-weighting of G is equitable irregular if |Sφ (u)−Sφ (v)| ≤ 1, for every pair of adjacent vertices u and v in G. Theequitable irregular strength of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G and is denoted by Se (G). In this paper, we discuss the equitable irregularity of Polar grid and Mongolian tent graphs

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“…Definition 2.1. [5] The polar grid graph P m,n is the graph consists of n copies of circles C m which will be numbered from the inner most circle to the outer circle as…”

Section: Resultsmentioning

confidence: 99%

Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph

Gayathri,

Saravanakumar

2024

Proyecciones (Antofagasta)

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“…A function f is called an edge even graceful labeling of a graph , is injective. This type of graph labeling was first introduced by Elsonbaty and Daoud in 2017 [24,25]. For a summary of the results on these five types of graceful labels as well as all known labeling techniques, see Reference [26].…”

Section: Cylinder Grid Graphmentioning

confidence: 99%

Edge Even Graceful Labeling of Cylinder Grid Graph

Elsonbaty

Daoud

2019

Symmetry

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Edge even graceful labeling (e.e.g., l.) of graphs is a modular technique of edge labeling of graphs, introduced in 2017. An e.e.g., l. of simple finite undirected graph G = ( V ( G ) , E ( G ) ) of order P = | ( V ( G ) | and size q = | E ( G ) | is a bijection f : E ( G ) → { 2 , 4 , … , 2 q } , such that when each vertex v ∈ V ( G ) is assigned the modular sum of the labels (images of f ) of the edges incident to v , the resulting vertex labels are distinct mod 2 r , where r = max ( p , q ) . In this work, the family of cylinder grid graphs are studied. Explicit formulas of e.e.g., l. for all of the cases of each member of this family have been proven.

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“…In [10], Moussa and Badr demonstrated the odd gracefulness of ladder graphs. The authors of [11,12] stressed the importance of the edge even graceful labeling. Deb and Limaye talked about the elegant labelings of triangular snakes in [13], and Diefenderfer et al examined the prime vertex labelings of various graph families in [14].…”

Section: Introductionmentioning

confidence: 99%

Enhanced Effectiveness in Various Ladder Graphs Based on the F-Centroidal Meanness Criterion

Rajesh Kannan,

Murali Krishnan,

Loganathan

et al. 2023

Mathematics

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Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a richer analysis and interpretation of the graph. Graph labeling in ladder graphs has a wide range of applications in engineering, computer science, physics, biology, and other fields. It can be applied to various problem domains, such as image processing, wireless sensor networks, VLSI design, bioinformatics, social network analysis, transportation networks, and many others. The versatility of ladder graphs and the ability to apply graph labeling to them make them a powerful tool for modeling and analyzing diverse systems. If a function Υ is an injective vertex assignment in {1,2,…q+1} and the inductive edge assignment function Υ* in {1,2,…q} is expressed as a graph with q edges, defined as Υ*(uv)=2[Υ(u)2+Υ(u)Υ(v)+Υ(v)2]3[Υ(u)+Υ(v)], then the function is referred to as F-centroidal mean labeling. This is known as the F-centroidal mean criterion. Here, we have determined the F-centroidal mean criteria of the graph ladder, slanting ladder, triangular ladder, TLn∘Sm, SLn∘Sm for m≤2, double-sided step ladder, Dn*, and diamond ladder.

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Edge Even Graceful Labeling of Polar Grid Graphs

Cited by 9 publications

References 9 publications

Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph

Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph

Edge Even Graceful Labeling of Cylinder Grid Graph

Enhanced Effectiveness in Various Ladder Graphs Based on the F-Centroidal Meanness Criterion

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