Workshop on “Algebraic Graph Theory”

Summary of the Tianyuan Mathematical Research Center Workshop on “Algebraic Graph Theory”

The Tianyuan Mathematical Research Center Workshop on Algebraic Graph Theory was held from January 25 to January 31, 2026. The workshop was convened by Professors Jinxin Zhou (Beijing Jiaotong University), Caiheng Li (Southern University of Science and Technology), and Binzhou Xia (The University of Melbourne). It brought together 47 participants from leading universities and research institutions in mainland China, Slovakia, and Korea, fostering a focused and collaborative environment for advancing research on graph symmetry, spectral properties of graphs, and related topics in algebraic graph theory.

The scientific program covered a broad range of core and emerging topics in the field, including recent progress in extremal and spectral graph theory; the construction and classification of symmetric graphs or digraphs; the role of finite groups—particularly simple and almost simple groups—in the study of graph symmetry; the structural theory of Cayley graphs and graph coverings; and interactions with geometry, combinatorial designs, and permutation groups. Several presentations reported new constructions, classification results, or refined criteria for long-standing problems, reflecting both technical depth and conceptual advances in the area.

In addition to the formal talks, the workshop featured four themed open discussion sessions devoted to open problems and prospective research directions in algebraic graph theory. These discussions focused on topics such as the structural analysis of symmetric and half-arc-transitive graphs, classification strategies for graphs admitting prescribed group actions, the interplay between algebraic and spectral methods, and possible approaches to resolving several outstanding problems. The discussion sessions encouraged active participation and facilitated in-depth exchanges of ideas among participants.

The workshop brought together experts and researchers from a wide range of institutions, while also providing valuable opportunities for early-career researchers to present their work and engage directly with senior scholars. Through high-quality presentations and extensive discussions, participants gained a clearer understanding of the current research landscape and future directions in algebraic graph theory.

Overall, the workshop effectively promoted academic exchange and collaboration within the community. It contributed to the advancement of research on frontier problems in algebraic graph theory and played a constructive role in supporting the development of young researchers.

Participants expressed their sincere appreciation for the excellent academic environment and strong organizational support provided by the Tianyuan Mathematical Research Center. The interactions and collaborations fostered during the workshop are expected to have a lasting impact on future research. The organizers gratefully acknowledge the contributions of all speakers, participants, and staff members whose efforts ensured the success of the event.