Title: Edge fixed edge Steiner number of a graph

Authors: M. Perumalsamy; P. Arul Paul Sudhahar; J. John; R. Vasanthi

Addresses: Department of Mathematics, Alagappa Chettiar Government College of Engineering and Technology, Karaikudi-3, Tamilnadu, India ' Department of Mathematics, Rani Anna Govt. College for Women, Tirunelveli-8, Tamilnadu, India ' Department of Mathematics, Government College of Engineering, Tirunelveli, Tamilnadu, India ' Department of Mathematics, Alagappa Chettiar Government College of Engineering and Technology, Karaikudi-3, Tamilnadu, India

Abstract: For a non-empty set W of vertices in a connected graph G, the Steiner distance d(W) of W is the minimum size of a connected sub-graph of G containing W. S(W) denotes the set of vertices that lies in Steiner W-trees. Steiner set of a graph was introduced by Chartrand and Zhang (2002). An edge Steiner set of a graph was introduced by Santhakumaran and John (2007). In this paper, we introduce edge fixed edge Steiner set and study some of the characteristics of edge fixed edge Steiner number and provide the bounds for edge fixed edge Steiner number. Also we prove the existence theorem.

Keywords: Steiner set; edge fixed Steiner set; Steiner number; edge fixed Steiner number; edge fixed edge Steiner set; edge fixed edge Steiner number.

DOI: 10.1504/IJCSYSE.2019.101706

International Journal of Computational Systems Engineering, 2019 Vol.5 No.4, pp.230 - 234

Received: 13 Nov 2017
Accepted: 08 May 2018
Published online: 22 Aug 2019 *

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