Rainbow Connection Number of Graph Power and Graph Products

Basavaraju, Manu and Chandran, Sunil L and Rajendraprasad, Deepak and Ramaswamy, Arunselvan (2014) Rainbow Connection Number of Graph Power and Graph Products. In: GRAPHS AND COMBINATORICS, 30 (6). pp. 1363-1382.

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Abstract

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely the Cartesian product, the lexicographic product and the strong product) and the operation of taking the power of a graph. In this direction, we show that if G is a graph obtained by applying any of the operations mentioned above on non-trivial graphs, then rc(G) a parts per thousand currency sign 2r(G) + c, where r(G) denotes the radius of G and . In general the rainbow connection number of a bridgeless graph can be as high as the square of its radius 1]. This is an attempt to identify some graph classes which have rainbow connection number very close to the obvious lower bound of diameter (and thus the radius). The bounds reported are tight up to additive constants. The proofs are constructive and hence yield polynomial time -factor approximation algorithms.

Item Type:	Journal Article
Publication:	GRAPHS AND COMBINATORICS
Publisher:	SPRINGER JAPAN KK
Additional Information:	Copy right for this article belongs to the SPRINGER JAPAN KK, CHIYODA FIRST BLDG EAST, 3-8-1 NISHI-KANDA, CHIYODA-KU, TOKYO, 101-0065, JAPAN
Keywords:	Cartesian product; Lexicographic product; Strong product; Graph power; Rainbow coloring
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	04 Dec 2014 04:47
Last Modified:	04 Dec 2014 04:47
URI:	http://eprints.iisc.ac.in/id/eprint/50359

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