具有n-4个悬挂点的三圈图补图的最小特征值

Minimum eigenvalue of the complement of tricyclic graphs with n-4 pendent vertexes

为了讨论给定阶数为n且具有n-4个悬挂点的三圈图补图图类中邻接矩阵的最小特征值,刻画其最小特征值达到极小的唯一图。在只考虑简单无向连通图的基础上,从补图的结构出发研究图的最小特征值,通过运用相关知识点分析论证了当值为λ(G(「(n-4)/2」,「(n-4)/2)」^C)时,给定阶数为n且具有n-4个悬挂点的三圈图补图图类中邻接矩阵的最小特征值达到极小的唯一图。结果表明:结合图邻接矩阵是表示顶点之间相邻关系的矩阵,它的最小特征值为图的最小特征值,较好地刻画图的本质性质。研究得出的具有n-4个悬挂点的三圈图补图的最小特征值达到极小的唯一图,为后续进一步研究补图图类中邻接矩阵的最小特征值提供了一定的借鉴价值。

In order to discuss the minimum eigenvalue of adjacency matrix in the class of complementary graphs of the tricyclic graph with a given order of n and n-4 pendent vertexes,the unique graph whose minimum eigenvalue reaches the minimum is characterized.Based on the simple undirected connected graph,the minimum eigenvalue of the graph is studied from the structure of the complement graph,and the minimum eigenvalue of the adjacency matrix in the complement graph class of the tricyclic graph with a given order of n and n-4 pendent vertexes reaches the minimum unique graph when the value isλ(G(「(n-4)/2」,「(n-4)/2)」^C).The result shows that the associative graph adjacency matrix is a matrix which represents the adjacency between vertices,and its minimum eigenvalue is the minimum eigenvalue of graph,which can describe the essential properties of graph well.The conclusion from this research shows that the minimum eigenvalue of the complement graph of the tricyclic graph with a given order of n and n-4 pendent vertexes reaches the minimum eigenvalue,which provides certain reference for further study of the minimum eigenvalue of the adjacency matrix in the complement graph class.