Prof. Indah Emilia Wijayanti and Felicia Servina Djuang, a Ph.D. student, from our laboratory attended the Algebra, Geometry, Combinatorics, and Applications Conference (ALGECOM 2026) held on 10–11 April 2026 at De La Salle University, Manila, Philippines.
Djuang presented her research on “Automorphism Group of Shuriken Graphs Derived From The Clean Graphs of Rings”. In her presentation, Djuang discussed a research project at the intersection of algebra and graph theory. The work focuses on two graphs associated with a finite ring with identity: the idempotent graph and the clean graph. The idempotent graph is constructed from the non-trivial idempotent elements of a ring, while the clean graph combines idempotent elements and units to form a richer graph structure.
A central object of her study is the shuriken graph operation, a graph construction that naturally arises from the structure of clean graphs and depends on the associated idempotent graph. The presentation explored how this operation transforms a given graph and how its structural properties can be analyzed using graph-theoretic methods.
The main focus of the research was the study of the automorphism groups of shuriken graphs. In particular, Felicia investigated how the symmetries of a shuriken graph are related to the automorphism group of its underlying base graph. Understanding these relationships provides insight into how algebraic structures influence graph symmetries and contributes to the broader study of algebraic graph theory.
The presentation generated fruitful discussions among conference participants and highlighted the connection between ring theory, graph theory, and group actions. Through her participation in ALGECOM 2026, Felicia had the opportunity to share her research with an international audience and engage with researchers working in related areas of algebra and combinatorics.