CAJ | 학술논문

设G是1个无向的简单图,ν表示G的阶数,m_G(ν)表示ν作为G的Laplacian矩阵的特征值的重数.得到了Laplacian谱半径等于阶数的所有c圈图,研究了c与m_G(ν)之间的关系.给出了当G是森林、单圈图、双圈图、三圈图、四圈图时m_G(ν)的取值范围,并确定了m_G(ν)(≥1)在该取值范围内取不同值时的所有图.
설G시1개무향적간단도,ν표시G적계수,m_G(ν)표시ν작위G적Laplacian구진적특정치적중수.득도료Laplacian보반경등우계수적소유c권도,연구료c여m_G(ν)지간적관계.급출료당G시삼림、단권도、쌍권도、삼권도、사권도시m_G(ν)적취치범위,병학정료m_G(ν)(≥1)재해취치범위내취불동치시적소유도.
G is a simple undirected graph of order v.m_G(ν) denotes the multiplicity of ν being an eigenvalue of Laplacian matrix.In this paper, the c cyclic graph whose largest eigenvalue of its Laplacian matrix equals ν is obtained, and the relation of c and m_G(ν) is studied.Moreover, the range of m_G(ν) is obtained when G is a forest, a unicyclic graph, a bicyclic graph, a tricyclic graph and a tetracyclic graph, respectively, and the graph is determined when m_G(ν)(≥1) takes different value in its range.