Some Steiner concepts on lexicographic products of graphs-Reference-Cited by-同舟云学术

Some Steiner concepts on lexicographic products of graphs

Published:2014-10-10 Issue:04 Volume:06 Page:1450060
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Anand Bijo S.¹²,Changat Manoj³,Peterin Iztok⁴,Narasimha-Shenoi Prasanth G.⁵

Affiliation:

1. Department of Mathematics, Sree Narayana College for Women, Kollam-691001, India

2. Department of Futures Studies, University of Kerala, Trivandrum-695034, India

3. Department of Futures Studies, University of Kerala, Trivandrum-695581, India

4. University of Maribor, FEECS, Smetanova 17, 2000 Maribor, Slovenia

5. Department of Mathematics, Government College, Chittur, Palakkad-678 104, India

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830914500608

Reference27 articles.

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