Edge Even Graceful Labeling of Cylinder Grid Graph

Abstract

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.

New Perspectives on Classical Meanness of Some Ladder Graphs

“…Durai Baskar considered the logarithmic meanness in [14] and Rajesh Kannan et al characterized idea of exponential mean graphs in [15]. In addition, more concepts of ladder graphs and related concepts have been studied in [16][17][18][19][20][21][22][23][24]. Recently, Muhiuddin et al have applied various related concepts on graphs in different aspects (see, e.g., [25][26][27][28][29][30][31]).…”

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

“…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].…”

Extending of Edge Even Graceful Labeling of Graphs to Strong r -Edge Even Graceful Labeling

“…, 2q 􏼈 􏼉, defined as f * (x) � (􏽐 xy∈E(G) f(xy))mod(2k), is an injective function, where k � max(p, q). is type of graph labeling was first introduced by Elsonbaty and Daoud in 2017 [8,9]. ey introduced some path-and cycle-related graphs which are edge even graceful.…”