2025/01/28 by Natasha Jonoska, Jonoska, Natasha, Milé Krajčevski +3
Computer Science · Engineering · #Advanced Graph Neural Networks #Combinatorics (math.CO) #FOS: Mathematics #Graph Theory and Algorithms #VLSI and FPGA Design Techniques
paper · pdf · doi:10.48550/arxiv.2501.17135
openalex publication_date 2025/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider voltage digraphs, here referred to as graphs, whose edges are labeled with elements from a given group, and explore their derived graphs. Given two voltage graphs, with voltages in abelian groups, we establish a necessary and sufficient condition for their two derived graphs to be isomorphic. This condition requires: (1) the existence of a voltage graph that covers both given graphs, and (2) when the two sets of voltages are lifted to the common cover, the correspondence between these sets of voltages determines an isomorphism between the groups generated by these voltages. We show that conditions (1) and (2) are decidable, and provide a method for constructing the common cover and for lifting the voltage assignments.