The subtree number, together with its refined variants—including the BC-subtree number and, more recently, the α-subtree number—has emerged as an important family of structure-based topological indices. These indices capture essential branching properties of graphs and have found broad applications across multiple disciplines. A fundamental scientific question underlying this line of research is: How can we characterize the structural complexity of a graph through counting its connected substructures, and to what extent can such counting frameworks be generalized?

In this talk, we first provide an overview of enumeration algorithms for the subtree number and the BC-subtree number, and discuss related extremal problems as well as their connections with classical indices such as the Wiener index. We then introduce our recent work on a natural generalization—the leaf-distance granular regular subtree number, i.e., the α-subtree number—which offers a flexible measurement framework and provides new insights into graph structure. Finally, we extend the discussion to the subpath number, interpreting it as a complementary generalization that captures linear substructures within the same counting paradigm. Together, these developments contribute to a broader understanding of the subtree number problem and open new directions for theoretical exploration in graph enumeration.

Yu Yang: Ph.D., Professor, PhD Supervisor, major in Computer Application Technology. He serves as Associate Dean of the School of Artificial Intelligence, Pingdingshan University. He is a Distinguished Member of the China Computer Federation (CCF), an Academic and Technical Leader of Henan Province, an Academic and Technical Leader of the Department of Education of Henan Province, a Scientific and Technological Innovation Talent of Henan Universities, a Chief Science Popularization Expert of Henan Province, and an evaluation expert for national young talent programs. He is also Director of the Henan International Joint Laboratory of Molecular Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Fine Particulate Matter (PM2.5), a member of the Council of the Henan Computer Federation, a member of the Council of the North American Branch of Henan Overseas Returned Scholars Association, a supervisor of outstanding degree theses in Henan Province, and a reviewer for Mathematical Reviews.

His main research interests include artificial intelligence, smart healthcare, and graph computing. He has led more than 10 research projects, including those funded by the National Natural Science Foundation of China. He has published over 20 high-level papers in CCF Category A journals and CAS Division 1 journals, and has authored three textbooks and monographs. He holds over 10 authorized patents and software copyrights. He serves as a reviewer for internationally renowned SCI journals such as TCS, and is an overseas expert for faculty promotion evaluations at several international universities. He has received the Second Prize in the Henan Provincial Undergraduate University Teaching Innovation Competition, and has served as the supervising instructor for students who won the Third Prize in the National Finals and the First Prize in the Provincial Competition of the Blue Bridge Cup Competition.