On b-edge consecutive edge labeling of some regular tree

<div class="page" title="Page 1"><div class="layoutArea"><div class="column">Let G = (V, E) be a finite (non-empty), simple, connected and undirected graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪ E to the integers 1, 2, . . . , n + e, with the property that for every xy ∈ E, α(x) + α(y) + α(xy) = k, for some constant k. Such a labeling is called a b-edge consecutive edge magic total if α(E) = {b + 1, b + 2, . . . , b + e}. In this paper, we proved that several classes of regular trees, such as regular caterpillars, regular firecrackers, regular caterpillar-like trees, regular path-like trees, and regular banana trees, have a b-edge consecutive edge magic labeling for some 0 < b < |V |.</div></div></div>

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Power-3 Heronian Mean Labeling of Graphs

International Journal of Engineering and Advanced Technology - Regular Issue ◽

10.35940/ijeat.d7831.049420 ◽

2020 ◽

Vol 9 (4) ◽

pp. 1359-1361

Keyword(s):

Undirected Graph ◽

Heronian Mean ◽

Edge Labeling

Let be an undirected graph having vertices and edges. Now, defining a function say, is called Power-3 Heronian Mean Labeling of a graph if we could able to label the vertices with dissimilar elements from such that it induces an edge labeling defined as, is dissimilar for all the edges (i,e.) It intimates that the dissimilar vertex labeling induces a dissimilar edge labeling on the graph. The graph which owns Power-3 Heronian Mean Labeling is called an Power-3 Heronian Mean Graph. In this, we have advocated the Power-3 Heronian Mean Labeling of some standard graphs like Path, Comb, Caterpillar, Triangular Snake, Quadrilateral Snake and Ladder.

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Edge Even Graceful Labeling of Cylinder Grid Graph

Symmetry ◽

10.3390/sym11040584 ◽

2019 ◽

Vol 11 (4) ◽

pp. 584 ◽

Cited By ~ 2

Author(s):

Ahmed A. Elsonbaty ◽

Salama Nagy Daoud

Keyword(s):

Undirected Graph ◽

Grid Graph ◽

Explicit Formulas ◽

Graceful Labeling ◽

Grid Graphs ◽

The Family ◽

Edge Labeling

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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On SD-Prime Labelings of Some One Point Unions of Gears

Symmetry ◽

10.3390/sym13050849 ◽

2021 ◽

Vol 13 (5) ◽

pp. 849

Author(s):

Wai-Chee Shiu ◽

Gee-Choon Lau

Keyword(s):

Undirected Graph ◽

Prime Labeling ◽

Edge Labeling

Let G=(V(G),E(G)) be a simple, finite and undirected graph of order n. Given a bijection f:V(G)→{1,…,n}, and every edge uv in E(G), let S=f(u)+f(v) and D=|f(u)−f(v)|. The labeling f induces an edge labeling f′:E(G)→{0,1} such that for an edge uv in E(G), f′(uv)=1 if gcd(S,D)=1, and f′(uv)=0 otherwise. Such a labeling is called an SD-prime labeling if f′(uv)=1 for all uv∈E(G). We provide SD-prime labelings for some one point unions of gear graphs.

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