Upper double monophonic number of a graph

  • A. P. Santhakumaran Hindustan Institute of Technology and Science.
  • T. Venkata Raghu Sasi Institute of Technology and Engineering.

Resumen

A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u − v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm⁺(G). Some general properties satisfied by upper double monophonic sets are discussed. It is proved  that for a connected graph G of order n, dm(G) = n if and only if dm⁺(G) = n. It is also proved that dm(G) = n − 1 if and only if dm⁺ (G) = n − 1 for a non-complete graph G of order n with a full degree vertex. For any positive integers 2 ≤ a ≤ b, there exists a connected graph G with dm(G) = a and dm⁺(G) = b.

Biografía del autor

A. P. Santhakumaran, Hindustan Institute of Technology and Science.
Departamento de Matemáticas.
T. Venkata Raghu, Sasi Institute of Technology and Engineering.
Departamento de Ciencias Aplicadas y Humanidades.

Citas

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[5] A. P. Santhakumaran and T. Jebaraj, The upper double geodetic number of a graph, Malaysian Journal of Science 30 (3): 225- 229, (2011).

[6] A. P. Santhakumaran and T. Jebaraj, The double geodetic number of a graph, Discuss. Math. Graph Theory, 32, pp. 109-119, (2012).

[7] A. P. Santhakumaran and T. Venkata Raghu, The double monophonic number of a graph, International Journal of Computational and Applied Mathematics, 11 (1), pp. 21-26, (2016).
Publicado
2018-06-06
Cómo citar
Santhakumaran, A., & Venkata Raghu, T. (2018). Upper double monophonic number of a graph. Proyecciones. Revista De Matemática, 37(2), 295-304. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2929
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Artículos