| dc.creator | Santhakumaran, A. P. | |
| dc.creator | Balaganesan, P. | |
| dc.date | 2018-03-15 | |
| dc.date.accessioned | 2019-11-14T12:00:57Z | |
| dc.date.available | 2019-11-14T12:00:57Z | |
| dc.identifier | https://www.revistaproyecciones.cl/article/view/2778 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/113598 | |
| dc.description | A connected graph G = (V, E) of order atleast two, with order p and size q is called vertex-graceful if there exists a bijection f : V → {1, 2, 3, ··· p} such that the induced function f ∗ : E → {0, 1, 2, ··· q − 1} defined by f ∗ (uv) = (f(u) + f(v))(mod q) is a bijection. The bijection f is called a vertex-graceful labeling of G. A subset S of the set of natural numbers N is called consecutive if S consists of consecutive integers. For any set X, a mapping f : X → N is said to be consecutive if f(X) is consecutive. A vertex-graceful labeling f is said to be strong if the function f1 : E → N defined by f1(e) = f(u)+ f(v) for all edges e = uv in E forms a consecutive set. It is proved that one vertex union of odd number of copies of isomorphic caterpillars is vertex-graceful and any caterpillar is strong vertex-graceful. It is proved that a spider with even number of legs (paths) of equal length appended to each vertex of an odd cycle is vertex-graceful. It is also proved that the graph lA(mj , n) is vertex-graceful for both n and l odd, 0 ≤ i ≤ n − 1, 1 ≤ j ≤ mi. Further, it is proved that the graph A(mj , n) is strong vertex-graceful for n odd, 0 ≤ i ≤ n − 1, 1 ≤ j ≤ mi. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.relation | https://www.revistaproyecciones.cl/article/view/2778/2347 | |
| dc.rights | Derechos de autor 2018 Proyecciones. Journal of Mathematics | es-ES |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | es-ES |
| dc.source | Proyecciones. Journal of Mathematics; Vol 37 No 1 (2018); 19-43 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 37 Núm. 1 (2018); 19-43 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.subject | Caterpillar | en-US |
| dc.subject | One vertex union graphs | en-US |
| dc.subject | Regular spider | en-US |
| dc.subject | Actinia graph | en-US |
| dc.subject | Vertex-graceful labeling | en-US |
| dc.subject | Strong vertex-graceful labeling | en-US |
| dc.title | Vertex graceful labeling of some classes of graphs. | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Artículo revisado por pares | es-ES |
