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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

TITUS, P.  and  VANAJA, S. Eldin. Edge fixed monophonic number of a graph. Proyecciones (Antofagasta) [online]. 2017, vol.36, n.3, pp.363-372. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172017000300363.

For an edge xy in a connected graph G of order p ≥ 3, a set S V(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as the xy-monophonic number of G, denoted by mxy (G) . An xy-monophonic set of cardinality mxy (G) is called a mxy -set of G. We determine bounds for it and find the same for special classes of graphs. It is shown that for any three positive integers r, d and n ≥ 2 with 2 ≤ r ≤ d, there exists a connected graph G with monophonic radius r, monophonic diameter d and mxy (G) = n for some edge xy in G.

Keywords : Monophonic path; vertex monophonic number; edge fixed monophonic number.

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