Radio number for trees Original Research Article

Let G be a connected graph with diameter image. The radio number for G, denoted by image, is the smallest integer k such that there exists a function image with the following satisfied for all vertices u and image: image where image is the distance between u and image. We prove a lower bound for the radio number of trees, and characterize the trees achieving this bound. Moreover, we prove another lower bound for the radio number of spiders (trees with at most one vertex of degree more than two) and characterize the spiders achieving this bound. Our results generalize the radio number for paths obtained by Liu and Zhu.