Báo cáo viên: Phan Thị Hà Dương
Thời gian: 10h15 - 11h15, thứ 5 ngày 13 tháng 2 năm 2025
Địa điểm: Phòng 612, nhà A6, Viện Toán học
Tóm tắt: We study graph models of discrete dynamical systems, where the state space is represented by a directed graph in which each vertex has exactly one outgoing edge known as a functional graph. On the set of functional graphs, two operations, Serie (addition) and Parallel (multiplication), are defined, turning it into a commutative semiring. A key question we investigate is when a graph can be decomposed as a product of two other graphs, when a graph is a divisor of another, and what the quotient graphs look like. More precisely, we explore problems related to the divisors of a graph that can be expressed as a sum of cycles. Initially, we focus on cases where cycle lengths are powers of the same prime number. We then generalize this problem using a recurrence method based on the number of distinct prime factors appearing in the cycles. We provide algorithms to determine whether a sum of divisors is a divisor of another graph and analyze the computational complexity of this problem. |
