Randic index, radius, and diameter for cactus graphs
arXiv:2107.00071
Abstract
We study the Randic index for cactus graphs. It is conjectured to be bounded below by radius (for other than an even path), and it is known to obey several bounds based on diameter. We study radius and diameter for cacti then verify the radius bound and strengthen two diameter bounds for cacti. Along the way, we produce several other bounds for the Randic index in terms of graph size, order, and valency for several special classes of graphs, including chemical nontrivial cacti and cacti with starlike BC-trees.
23 pages, 6 figures; expanded Lemmas 3.2-3.3 and Theorem 4.6, corrected proof of Theorem 5.5, updated abstract