CAJ | 학술논문

边数等于点数加二的连通图称为三圈图.设△(G)和μ(G)分别表示图G的最大度和其拉普拉斯谱半径,设T(n)表示所有n阶三圈图的集合,证明了对于T(n)的两个图H1和H2,若△(H1)＞△(H2)且△(H1)≥n+7/2,则μ(H1)＞μ(H2).作为该结论的应用,确定了T(n)(n≥9)中图的第七大至第十九大的拉普拉斯谱半径及其相应的极图.
변수등우점수가이적련통도칭위삼권도.설△(G)화μ(G)분별표시도G적최대도화기랍보랍사보반경,설T(n)표시소유n계삼권도적집합,증명료대우T(n)적량개도H1화H2,약△(H1)＞△(H2)차△(H1)≥n+7/2,칙μ(H1)＞μ(H2).작위해결론적응용,학정료T(n)(n≥9)중도적제칠대지제십구대적랍보랍사보반경급기상응적겁도.
A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two.Let △(G) and μ(G) denote the maximum degree and the Laplacian spectral radius of a graph G,respectively.Let T(n) be the set of tricyclic graphs on n vertices.In this paper,it is proved that,for two graphs H1 and H2 in T(n),if △(H1) ＞ △(H2) and △(H1) ≥ n+7/2,then μ(H1) ＞ μ(H2).As an application of this result,we determine the seventh to the nineteenth largest values of the Laplacian spectral radii among all the graphs in T(n)(n ≥ 9) together with the corresponding graphs.