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Boxicity and cubicity of product graphs

Chandran, Sunil L and Imrich, Wilfried and Mathew, Rogers and Rajendraprasad, Deepak (2015) Boxicity and cubicity of product graphs. In: EUROPEAN JOURNAL OF COMBINATORICS, 48 (SI). pp. 100-109.

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Official URL: http://dx.doi.org/ 10.1016/j.ejc.2015.02.013

Abstract

The boxicity (cubicity) of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in R-k. In this article, we give estimates on the boxicity and the cubicity of Cartesian, strong and direct products of graphs in terms of invariants of the component graphs. In particular, we study the growth, as a function of d, of the boxicity and the cubicity of the dth power of a graph with respect to the three products. Among others, we show a surprising result that the boxicity and the cubicity of the dth Cartesian power of any given finite graph is, respectively, in O(log d/ log log d) and circle dot(d/ log d). On the other hand, we show that there cannot exist any sublinear bound on the growth of the boxicity of powers of a general graph with respect to strong and direct products. (C) 2015 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 24-28 OVAL RD, LONDON NW1 7DX, ENGLAND
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 22 Jun 2015 04:54
Last Modified: 22 Jun 2015 04:54
URI: http://eprints.iisc.ac.in/id/eprint/51713

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