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Rotary embeddings of Praeger-Xu graphs

刘鲁一 Luyi Liu

Southern University of Science and Technology

Time: 16:00-17:00 (GMT+8), Wednesday September 17th, 2025
Location: Zoom

Abstract: Rotary maps (orientably regular maps) are highly symmetric graph embeddings on orientable surfaces. In this talk, we introduce the classification of rotary maps whose underlying graphs are Praeger-Xu graphs, denoted \(\operatorname{C}(p,r,s)\), for any odd prime \(p\) that does not divide \(r\). We will establishe a one-to-one correspondence between the isomorphism classes of these maps and the multiplicity-free representations of the dihedral group \(\mathup{D}_{2r}\) over the finite field \(\mathbb{F}_p\). This work extends a recent classification for the case where \(p=2\).

Host: 甘芸松 Yunsong Gan