image-labeling of perfect elimination bipartite graphs Original Research Article

An image-labeling of a graph image is an assignment of nonnegative integers, called colors, to the vertices of image such that the difference between the colors assigned to any two adjacent vertices is at least two and the difference between the colors assigned to any two vertices which are at distance two apart is at least one. The span of an image-labeling image is the maximum color number that has been assigned to a vertex of image by image. The image-labeling number of a graph image, denoted as image, is the least integer image such that image has an image-labeling of span image. In this paper, we propose a linear time algorithm to image-label a chain graph optimally. We present constant approximation image-labeling algorithms for various subclasses of chordal bipartite graphs. We show that image for a chordal bipartite graph image, where image is the maximum degree of image. However, we show that there are perfect elimination bipartite graphs having image. Finally, we prove that computing image of a perfect elimination bipartite graph is NP-hard.