1. Some Steiner concepts on lexicographic products of graphs.
- Author
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Anand, Bijo S., Changat, Manoj, Peterin, Iztok, and Narasimha-Shenoi, Prasanth G.
- Subjects
- *
POLYNOMIALS , *BANDWIDTH allocation , *APPLIED mathematics , *STEINER systems , *LEXICOGRAPHY - Abstract
Let G be a graph and W a subset of V(G). A subtree with the minimum number of edges that contains all vertices of W is a Steiner tree for W. The number of edges of such a tree is the Steiner distance of W and union of all vertices belonging to Steiner trees for W form a Steiner interval. We describe both of these for the lexicographic product of graphs. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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