Even vertex equitable even labeling for snake related graphs.

Authors

Keywords:

Vertex equitable labeling, Even vertex equitable even labeling, Double quadrilateral snake, Double triangular snake

Abstract

Let G be a graph with p vertices and q edges and A = {0,2,4,···, q+1} if q is odd or A = {0,2,4,···,q} if q is even. A graph G is said to be an even 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 even vertex equitable even labeling is called an even vertex equitable even graph. In this paper, we prove that S(D(Qn)), S(D(Tn)), DA(Qm) ʘ nK1, DA(Tm) ʘ nK1, S(DA(Qn)) and S(DA(Tn)) are an even vertex equitable even graphs.

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Author Biographies

  • A. Lourdusamy, St. Xavier’s College (Autonomous).

    Department of Mathematics.

  • S. Jenifer Wency, St. Xavier’s College (Autonomous).

    Department of Mathematics.

  • F. Patrick, St. Xavier's College (Autonomous).

    Department of Mathematics.

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Published

2019-02-26

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Artículos

How to Cite

[1]
“Even vertex equitable even labeling for snake related graphs”., Proyecciones (Antofagasta, On line), vol. 38, no. 1, pp. 177–189, Feb. 2019, Accessed: Sep. 18, 2024. [Online]. Available: https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3418