Odd Vertex equitable even labeling of cyclic snake related graphs
Abstract Let G be a graph with p vertices and q edges and A = {1, 3, ..., q} if q is odd or A = {1, 3, ..., q + 1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V (G) → A that induces an edge labeling f∗ defin...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2018
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000400613 |
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| Sumario: | Abstract Let G be a graph with p vertices and q edges and A = {1, 3, ..., q} if q is odd or A = {1, 3, ..., q + 1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V (G) → A that induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the induced edge labels are 2, 4, ..., 2q where vf (a) be the number of vertices v with f(v) = a for a ∈ A. A graph that admits an odd vertex equitable even labeling is called an odd vertex equitable even graph. Here, we prove that the graph nC4-snake, CS(n1, n2, ..., nk), ni ≡ 0(mod4),ni ≥ 4, be a generalized kCn -snake, TÔQSn and TÕQSn are odd vertex equitable even graphs. |
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