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.
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Kathiresan, K.M., Arockiaraj, S., Gurusamy, R., Amutha, K. (2012). On the Steiner Radial Number of Graphs. In: Arumugam, S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2012. Lecture Notes in Computer Science, vol 7643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35926-2_7
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DOI: https://doi.org/10.1007/978-3-642-35926-2_7
Publisher Name: Springer, Berlin, Heidelberg
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