学术报告
Perfect codes in circulant graphs
题 目：Perfect codes in circulant graphs
报告人：Prof. Rongquan Feng (LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China)
摘要: A perfect code in a graph $/Gamma=(V, E)$ is a subset $C$ of $V$ that is an independent set such that every vertex in $V/C$ is adjacent to exactly one vertex in $C$. A total perfect code in $/Gamma$ is a subset $C$ of $V$ such thatevery vertex of $V$ is adjacent to exactly one vertex in $C$. A perfect code in the Hamming graph $H(n,q)$ agrees with a q-ary perfect 1-code of length $n$ in the classical setting. In this paper we give a necessary and sufficient condition for a circulant graph of degree $p-1$ to admit a perfect code, where $p$ is an odd prime. We also obtain anecessary and sufficient condition for a circulant graph of order $n$ and degree $p^l-1$ to have a perfect code, where $p$ is a prime and $p^l$ the largest power of $p$ dividing $n$. Similar results for total perfect codes are also obtained in the paper.
时间：5月17日（周二）上午10:00
地点：首都师大北一区教学楼317教室
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