边正则图和伪强正则图在图运算下的变换
The transformation of edge-regular and pseudo strongly regular graphs under graph operations
摘要：
如果下列条件成立，则称图$G$是参数为$(n,k,λ,μ)$的强正则图：（1）每个顶点都有$k$近邻;（2）$G$的任意两个相邻顶点都有$λ$公共近邻;（3）$G$的任意两个不相邻顶点都有$μ$公共近邻.本文研究了强正则图的两个较弱的概念。满足条件$(1)$和$(2)$的图称为带参数$(n,k,λ)$的边正则图.我们称满足条件$(1)$和$(3)$的图为带参数$(n,k,μ)$的伪强正则图。本文研究了各种图操作对边正则图和伪强正则图的影响。
英文摘要：
The graph $G$ is said to be strongly regular with parameters $(n,k,λ,μ)$ if the following conditions hold: (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have $λ$ common neighbours; (3) any two non-adjacent vertices of $G$ have $μ$ common neighbours. In this paper we study two weaker notions of strongly regular graphs. A graph satisfying the conditions $(1)$ and $(2)$ is called an edge-regular graph with parameters $(n,k,λ)$. We call a graph satisfying the conditions $(1)$ and $(3)$ a pseudo strongly regular graph with parameters $(n,k,μ)$. In this paper we study the impact of various graph operations on edge regular graphs and pseudo strongly regular graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
