新疆师范大学学报（自然科学版）2024，Vol.43Issue(4)：62-67,6.
图变换及其在图的最小特征值的应用
The Graft Transformations and Their Applications on the Least Eigenvalues of Graphs
摘要
Abstract
Suppose G is a connected simple graph with the vertex set V(G)={v1,v2,⋯,vn}.Then the adjacency matrix of G is A(G)=(aij)n×n,where aij=1 if vi is adjacent to vj,and otherwise aij=0.Since A(G)is real and symmetric,its eigenvalues can be arranged as λ1(G)≥λ2(G)≥⋯≥λn(G),and the eigenvalues of A(G)are also called the eigenvalues of G.In this paper we first give three graft transformations on the least eigenvalues of graphs are given and then as their applications two connected graphs on n≥12 vertices whose least eigenvalues can be minimum among the complements of all unicyclic graphs are given,which modifies the main result in literature[9].关键词
图变换/最小特征值/单圈图/补图Key words
Transformation/The least eigenvalue/Unicyclic graph/Complement of graph分类
数理科学引用本文复制引用
王东宜,冯小芸,张维娟,王国平..图变换及其在图的最小特征值的应用[J].新疆师范大学学报（自然科学版）,2024,43(4):62-67,6.基金项目
新疆维吾尔自治区自然科学基金项目(2023D01A38). （2023D01A38）
