Vertex equitable labeling of union of cyclic snake related graphs

P. Jeyanthi, A. Maheswari, M. Vijayalakshmi

Resumen


Let G be a graph with p vértices and q edges and A = {0,1, 2,..., [q/2]}. A vertex labeling f : V(G) → A induces an edge labeling f * defined by f *(uv) = f (u) + f (v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f (v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf(a) — vfb)| ≤ 1 and the induced edge labels are 1, 2, 3,...,q. In this paper, we prove that key graph KY(m, n), P(2.QSn), P(m.QSn), C(n.QSm), NQ(m) and K1,n X P2are vertex equitable graphs.

Palabras clave


Vertex equitable labeling; vertex equitable graph; comb graph; key graph; path union graph; quadrilateral snake graph; etiquetado equitativo de vértices; grafo de vértices equitativos; grafos curvos; grafos clave; grafo de unión de trayectorias.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172016000200003

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