BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 6 Sayı: 1, 75 - 86, 01.06.2016

Öz

Kaynakça

  • Buckley, F. and Harary. F., (1990), Distance in Graphs, Addison-Wesley, Redwood City, CA.
  • Chartrand, G., Escuadro, H. and Zhang, P., (2005), Detour Distance in Graphs, J. Combin. Math. Combin. Comput., 53, pp. 75-94.
  • Chartrand, G., Johns, G.L. and Zhang, P., (2003), The Detour Number of a Graph, Utilitas Mathe- matica 64, pp. 97-113.
  • Chartrand, G., Johns, G.L. and Zhang, P., (2004), On the Detour Number and Geodetic Number of a Graph, Ars Combinatoria, 72, pp. 3-15.
  • Harary, F., (1969), Graph Theory, Addison-Wesley.
  • Harary, F., Loukakis, E. and Tsouros, C., (1993), The Geodetic Number of a Graph, Math. Comput. Modeling, 17 (11), pp. 87-95.
  • Santhakumaran, A.P. and Titus, P., (2011), Monophonic distance in graphs, Discrete Mathematics, Algorithms and Applications, Vol. 3, No. 2, pp. 159-169.
  • Santhakumaran, A.P. and Titus, P., (2012),A Note on “Monophonic Distance in Graphs”, Discrete Mathematics, Algorithms and Applications, Vol. 4, No. 2, DOI: 10.1142/S1793830912500188.
  • Santhakumaran, A.P. and Titus, P. and Ganesamoorthy, K., (2014), On the Monophonic Number of a Graph, J. Appl. Math. & Informatics Vol. 32, No. 1 - 2, pp. 255 - 266.
  • Titus, P. and Ganesamoorthy, K., (2014), The Connected Monophonic Number of a Graph, Graphs and Combinatorics, 30, pp. 237245.
  • Titus, P. and Ganesamoorthy, K., On the Detour Monophonic Number of a Graph, Ars Combinatoria, to appear.
  • Titus, P., Ganesamoorthy, K. and Balakrishnan, P., (2013), The Detour Monophonic Number of a Graph, J. Combin. Math. Combin. Comput., 84, pp. 179-188.

THE CONNECTED DETOUR MONOPHONIC NUMBER OF A GRAPH

Yıl 2016, Cilt: 6 Sayı: 1, 75 - 86, 01.06.2016

Öz

For a connected graph G = V, E of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A longest x − y monophonic path is called an x − y detour monophonic path. A set S of vertices of G is a detour monophonic set of G if each vertex v of G lies on an x − y detour monophonic path, for some x and y in S. The minimum cardinality of a detour monophonic set of G is the detour monophonic number of G and is denoted by dm G . A connected detour monophonic set of G is a detour monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected detour monophonic set of G is the connected detour monophonic number of G and is denoted by dmc G . We determine bounds for dmc G and characterize graphs which realize these bounds. It is shown that for positive integers r, d and k ≥ 6 with r < d, there exists a connected graph G with monophonic radius r, monophonic diameter d and dmc G = k. For each triple a, b, p of integers with 3 ≤ a ≤ b ≤ p − 2, there is a connected graph G of order p, dm G = a and dmc G = b. Also, for every pair a, b of positive integers with 3 ≤ a ≤ b, there is a connected graph G with mc G = a and dmc G = b, where mc G is the connected monophonic number of G.

Kaynakça

  • Buckley, F. and Harary. F., (1990), Distance in Graphs, Addison-Wesley, Redwood City, CA.
  • Chartrand, G., Escuadro, H. and Zhang, P., (2005), Detour Distance in Graphs, J. Combin. Math. Combin. Comput., 53, pp. 75-94.
  • Chartrand, G., Johns, G.L. and Zhang, P., (2003), The Detour Number of a Graph, Utilitas Mathe- matica 64, pp. 97-113.
  • Chartrand, G., Johns, G.L. and Zhang, P., (2004), On the Detour Number and Geodetic Number of a Graph, Ars Combinatoria, 72, pp. 3-15.
  • Harary, F., (1969), Graph Theory, Addison-Wesley.
  • Harary, F., Loukakis, E. and Tsouros, C., (1993), The Geodetic Number of a Graph, Math. Comput. Modeling, 17 (11), pp. 87-95.
  • Santhakumaran, A.P. and Titus, P., (2011), Monophonic distance in graphs, Discrete Mathematics, Algorithms and Applications, Vol. 3, No. 2, pp. 159-169.
  • Santhakumaran, A.P. and Titus, P., (2012),A Note on “Monophonic Distance in Graphs”, Discrete Mathematics, Algorithms and Applications, Vol. 4, No. 2, DOI: 10.1142/S1793830912500188.
  • Santhakumaran, A.P. and Titus, P. and Ganesamoorthy, K., (2014), On the Monophonic Number of a Graph, J. Appl. Math. & Informatics Vol. 32, No. 1 - 2, pp. 255 - 266.
  • Titus, P. and Ganesamoorthy, K., (2014), The Connected Monophonic Number of a Graph, Graphs and Combinatorics, 30, pp. 237245.
  • Titus, P. and Ganesamoorthy, K., On the Detour Monophonic Number of a Graph, Ars Combinatoria, to appear.
  • Titus, P., Ganesamoorthy, K. and Balakrishnan, P., (2013), The Detour Monophonic Number of a Graph, J. Combin. Math. Combin. Comput., 84, pp. 179-188.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

P. Titus Bu kişi benim

A. P. Santhakumaran Bu kişi benim

K. Ganesamoorthy Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 1

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