Edge odd graceful labeling of some path and cycle related graphs

Daoud, S. N.

doi:10.1016/j.akcej.2017.03.001

Cited by 27 publications

(17 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The polargrid 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 C m and m copies of paths P n+1 intersected at the center vertex v 0 which will be numbered as P [19]. See also Daoud [20]. A function f is called an edge even graceful labeling of a graph G if : ( ) {2, 4,. is injective.…”

Section: Polar Grid Graph P Mnmentioning

confidence: 99%

See 1 more Smart Citation

Edge Even Graceful Labeling of Polar Grid Graphs

Daoud

2019

Symmetry

View full text Add to dashboard Cite

Edge Even Graceful Labelingwas first defined byElsonbaty and Daoud in 2017. An edge even graceful labeling of a simple graph G with p vertices and q edges is a bijection f from the edges of the graph to the set { 2 , 4 , … , 2 q } such that, when each vertex is assigned the sum of all edges incident to it mod 2 r where r = max { p , q } , the resulting vertex labels are distinct. In this paper we proved necessary and sufficient conditions for the polar grid graph to be edge even graceful graph.

show abstract

Section: Polar Grid Graph P Mnmentioning

confidence: 99%

“…This type of graph labeling first introducedby Solairaju and Chithra in 2009 [19]. See also Daoud [20].…”

Section: Introductionmentioning

confidence: 99%

Edge Even Graceful Labeling of Polar Grid Graphs

Daoud

2019

Symmetry

View full text Add to dashboard Cite

show abstract

“…Solairaju and Chithra [6] in 2009 introduced a labeling of G called edge odd graceful labeling, which is a bijection f from the set of edges EðGÞ to the set f1, 3, ⋯, 2q − 1g such that the induced map f * from VðGÞ to f0, 1, 2, ⋯, 2q − 1g given by f * ðuÞ = ð∑ uv∈EðGÞ f ðuvÞÞ mod ð2qÞ is an injective. For many results on this type of labeling, see [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Edge δ− Graceful Labeling for Some Cyclic-Related Graphs

Deen

Mohamed²

2020

Advances in Mathematical Physics

View full text Add to dashboard Cite

In this paper, we introduce a new type of labeling of a graph G with p vertices and q edges called edge δ− graceful labeling, for any positive integer δ, as a bijective mapping f of the edge set EG into the set δ,2δ,3δ,⋯,qδ such that the induced mapping f∗:VG→0,δ,2δ,3δ,⋯,qδ−δ, given by f∗u=∑uv∈EGfuvmodδk, where k=maxp,q, is an injective function. We prove the existence of an edge δ− graceful labeling, for any positive integer δ, for some cycle-related graphs like the wheel graph, alternate triangular cycle, double wheel graph Wn,n, the prism graph Πn, the prism of the wheel PWn, the gear graph Gn, the closed helm CHn, the butterfly graph Bn, and the friendship Frn.

show abstract

“…The idea of graph labelings was introduced by Rosa in [1]. Following this paper, other studies on different types of labelings (Odd graceful, Chordal graceful, Harmonious, edge odd graceful) introduced by many others [2][3][4]. A new type of labeling of a graph called an edge even graceful labeling has been introduced by Elsonbaty and Daoud [5].…”

Section: Introductionmentioning

confidence: 99%

Edge even graceful labeling of some graphs

Deen

2019

J Egypt Math Soc

View full text Add to dashboard Cite

Edge even graceful labeling is a new type of labeling since it was introduced in 2017 by Elsonbaty and Daoud (Ars Combinatoria 130:79-96, 2017). In this paper, we obtained an edge even graceful labeling for some path-related graphs like Y-tree, the double star B n,m , the graph K 1,2n : K 1,2m , the graph P 2n−1 K 2m , and double fan graph F 2,n. Also, we showed that some cycle-related graphs like the prism graph n , the graph C n n 2 , the flag FL n , the graph K 2 C n , the flower graph FL(n), and the double cycle {C n,n } are edge even graphs.

show abstract

Edge odd graceful labeling of some path and cycle related graphs

Cited by 27 publications

References 3 publications

Edge Even Graceful Labeling of Polar Grid Graphs

Edge Even Graceful Labeling of Polar Grid Graphs

Edge δ− Graceful Labeling for Some Cyclic-Related Graphs

Edge even graceful labeling of some graphs

Contact Info

Product

Resources

About