Advertisement

On the Steiner Radial Number of Graphs

  • K. M. Kathiresan
  • S. Arockiaraj
  • R. Gurusamy
  • K. Amutha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

The Steiner n-radial graph of a graph G on p vertices, denoted by SR n (G), has the vertex set as in G and n(2 ≤ n ≤ p) vertices are mutually adjacent in SR n (G) if and only if they are n-radial in G. While G is disconnected, any n vertices are mutually adjacent in SR n (G) if not all of them are in the same component. When n = 2, SR n (G) coincides with the radial graph R(G). For a pair of graphs G and H on p vertices, the least positive integer n such that SR n (G) ≅ H, is called the Steiner completion number of G over H. When H = K p , the Steiner completion number of G over H is called the Steiner radial number of G. In this paper, we determine 3-radial graph of some classes of graphs, Steiner radial number for some standard graphs and the Steiner radial number for any tree. For any pair of positive integers n and p with 2 ≤ n ≤ p, we prove the existence of a graph on p vertices whose Steiner radial number is n.

Keywords

n-radius n-diameter Steiner n-radial graph Steiner completion number Steiner radial number 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Buckley, F., Harary, F.: Distance in graphs. Addison-Wesley, Reading (1990)zbMATHGoogle Scholar
  2. 2.
    Chartrand, G., Oellermann, O.R., Tian, S., Zou, H.B.: Steiner distance in graphs. Casopis Pro Pestovani Matematiky 114(4), 399–410 (1989)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Day, D.P., Oellermann, O.R., Swart, H.C.: Steiner distance-hereditary graphs. SIAM J. Discrete Math. 7, 437–442 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Kathiresan, K.M., Marimuthu, G.: A study on radial graphs. Ars Combin. 96, 353–360 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Oellermann, O.R., Tian, S.: Steiner centers in graphs. J. Graph Theory 14(5), 585–597 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Raines, M., Zhang, P.: The Steiner distance dimension of graphs. Australasian J. Combin. 20, 133–143 (1999)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • K. M. Kathiresan
    • 1
  • S. Arockiaraj
    • 2
  • R. Gurusamy
    • 2
  • K. Amutha
    • 3
  1. 1.Center for Research and Post Graduate Studies in MathematicsAyya Nadar Janaki Ammal CollegeSivakasiIndia
  2. 2.Department of Mathematics, Mepco Schlenk Engineering CollegeMepco Engineering CollegeSivakasiIndia
  3. 3.Department of MathematicsSri Parasakthi CollegeCourtallamIndia

Personalised recommendations