Edge δ− Graceful Labeling for Some Cyclic-Related Graphs
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∈EGfuv...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/6273245 |
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| author | Mohamed R. Zeen El Deen |
| author_facet | Mohamed R. Zeen El Deen |
| author_sort | Mohamed R. Zeen El Deen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f94565e6940c4f0d80063c1ee7b32f4e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f94565e6940c4f0d80063c1ee7b32f4e2025-02-03T01:01:30ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/62732456273245Edge δ− Graceful Labeling for Some Cyclic-Related GraphsMohamed R. Zeen El Deen0Department of Mathematics, Faculty of Science, Suez University, Suez 43527, EgyptIn 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.http://dx.doi.org/10.1155/2020/6273245 |
| spellingShingle | Mohamed R. Zeen El Deen Edge δ− Graceful Labeling for Some Cyclic-Related Graphs Advances in Mathematical Physics |
| title | Edge δ− Graceful Labeling for Some Cyclic-Related Graphs |
| title_full | Edge δ− Graceful Labeling for Some Cyclic-Related Graphs |
| title_fullStr | Edge δ− Graceful Labeling for Some Cyclic-Related Graphs |
| title_full_unstemmed | Edge δ− Graceful Labeling for Some Cyclic-Related Graphs |
| title_short | Edge δ− Graceful Labeling for Some Cyclic-Related Graphs |
| title_sort | edge δ graceful labeling for some cyclic related graphs |
| url | http://dx.doi.org/10.1155/2020/6273245 |
| work_keys_str_mv | AT mohamedrzeeneldeen edgedgracefullabelingforsomecyclicrelatedgraphs |