Edge fixed monophonic number of a graph.

• Autores: P. Titus, S. Eldin Vanaja
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 36, Nº. 3, 2017, págs. 363-372
• Idioma: inglés
• DOI: 10.4067/s0716-09172017000300363
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• Resumen

  • For an edge xy in a connected graph G of order p ≥ 3, a set SCV(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.

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