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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

JEYANTHI, P.; MAHESWARI, A.  and  VIJAYALAKSHMI, M.. Vertex equitable labeling of union of cyclic snake related graphs. Proyecciones (Antofagasta) [online]. 2016, vol.35, n.2, pp.177-186. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172016000200003.

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.

Keywords : Vertex equitable labeling; vertex equitable graph; comb graph; key graph; path union graph; quadrilateral snake graph.

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