Vertex graceful labeling of some classes of graphs
Abstract: 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 ʄ : V → { 1, 2, 3, ··· p } such that the induced function ʄ*: E → { 0, 1, 2, ··· q-1} defined by ʄ*(uv) = (@...
Guardado en:
| Autores principales: | , |
|---|---|
| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2018
|
| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100019 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:scielo:S0716-09172018000100019 |
|---|---|
| record_format |
dspace |
| spelling |
oai:scielo:S0716-091720180001000192018-03-13Vertex graceful labeling of some classes of graphsSanthakumaran,A. P.Balaganesan,P. Caterpillar one vertex union graphs regular spider actinia graph vertex-graceful labeling strong vertex-graceful labeling Abstract: 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 ʄ : V → { 1, 2, 3, ··· p } such that the induced function ʄ*: E → { 0, 1, 2, ··· q-1} defined by ʄ*(uv) = (ʄ(u)+ ʄ(v)) (mod q) is a bijection. The bijection ʄ 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 ʄ : X → N $ is said to be consecutive if ʄ(X) is consecutive. A vertex-graceful labeling ʄ is said to be strong if the function ʄ1: E → N defined by ʄ1(e)= ʄ(u) + ʄ(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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.1 20182018-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100019en10.4067/S0716-09172018000100019 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Caterpillar one vertex union graphs regular spider actinia graph vertex-graceful labeling strong vertex-graceful labeling |
| spellingShingle |
Caterpillar one vertex union graphs regular spider actinia graph vertex-graceful labeling strong vertex-graceful labeling Santhakumaran,A. P. Balaganesan,P. Vertex graceful labeling of some classes of graphs |
| description |
Abstract: 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 ʄ : V → { 1, 2, 3, ··· p } such that the induced function ʄ*: E → { 0, 1, 2, ··· q-1} defined by ʄ*(uv) = (ʄ(u)+ ʄ(v)) (mod q) is a bijection. The bijection ʄ 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 ʄ : X → N $ is said to be consecutive if ʄ(X) is consecutive. A vertex-graceful labeling ʄ is said to be strong if the function ʄ1: E → N defined by ʄ1(e)= ʄ(u) + ʄ(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. |
| author |
Santhakumaran,A. P. Balaganesan,P. |
| author_facet |
Santhakumaran,A. P. Balaganesan,P. |
| author_sort |
Santhakumaran,A. P. |
| title |
Vertex graceful labeling of some classes of graphs |
| title_short |
Vertex graceful labeling of some classes of graphs |
| title_full |
Vertex graceful labeling of some classes of graphs |
| title_fullStr |
Vertex graceful labeling of some classes of graphs |
| title_full_unstemmed |
Vertex graceful labeling of some classes of graphs |
| title_sort |
vertex graceful labeling of some classes of graphs |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2018 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100019 |
| work_keys_str_mv |
AT santhakumaranap vertexgracefullabelingofsomeclassesofgraphs AT balaganesanp vertexgracefullabelingofsomeclassesofgraphs |
| _version_ |
1718439831308075008 |