Rainbow Connection Number and Radius

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) <= r(r + 2). We demonstrate that this bound is the best possible for rc(G) as a function of r, not just for bridgeless graphs, but also for graphs of any stronger connectivity. It may be noted that for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius (Star graph for instance). We further show that for every bridgeless graph G with radius r and chordality (size of a largest induced cycle) k, rc(G) <= rk. It is known that computing rc(G) is NP-Hard [Chakraborty et al., 2009]. Here, we present a (r+3)-factor approximation algorithm which runs in O(nm) time and a (d+3)-factor approximation algorithm which runs in O(dm) time to rainbow colour any connected graph G on n vertices, with m edges, diameter d and radius r.Comment: Revised preprint with an extra section on an approximation algorithm. arXiv admin note: text overlap with arXiv:1101.574

Steganography Images Detection using Different Steganalysis Techniques with Markov Chain Features

Steganography is the art of covered or hidden writing It is used for criminal activities applications environment In this paper we focus on implementation of effective detection technique is an essential task in digital images Previously many number of detection techniques are available for steganography images After implementation of all approaches also again some challenges are available This paper presents comparative study in between different steganalysis techniques Different techniques are providing different results Analyze of all techniques detection and embedding performance results Finally we can decide one best steganalysis technique It saves time and increases accuracy compare to all previous method