Enumerating Subtrees of Flower and Sunflower Networks

Symmetry widely exists in many complex and real-world networks, with flower networks sunflower being two richly symmetric having practical applications due to their special structures. The number of subtrees (the subtree index) is closely related the reliable network design. Using a generating function, structural analysis techniques, auxiliary structure introduction, this paper presents functions Fln,m(n≥3,m≥2) Sfn,m(n≥3,m≥2) and, thus, solves computation indices Sfn,m(n≥3,m≥2). results provide fundamental efficient method for exploring novel features cyclic from index perspective. For instance, we conclude that under some parameter constraints, are more than networks.