单圈螺旋图谱半径的研究

Study on the Spectral Radius of Unicyclic Spiral Graphs

主要通过对Umax(n)中Uπ^*谱半径极值的研究,给出了其对应的单圈图度序列π的有关性质,并且进一步讨论了单圈图度序列π=(n-2,2,2,2,1,…,1)与其它单圈图度序列π’对应的Uπ^*和Uπ’^*的谱半径大小.(其中,Γ(π)表示具有单圈图度序列π的连通图的集合,Uπ^*表示Γ(π)中谱半径最大的图.Dn表示具有n个点的单圈图度序列π的集合,Umax(n)={Uπ^*|π∈Dn}.)

Through the study of the extreme value of the spectral radius of Uπ*in Umax(n),this paper mainly gives the relevant properties ofπ,the corresponding unicyclic degree sequence of Uπ*,and further compares the spectral radius of Uπ*and Uπ’*,whereπ=(n-2,2,2,2,1,···,1)andπ’is another unicyclic degree sequence.(Among them,denote byΓ(π)the set of connected graphs with unicyclic degree sequenceπand Uπ*the unicyclic graph with the largest spectral radius inΓ(π).Let Dn be the set of unicyclic degree sequences with n vertices and Umax(n)={Uπ*|π∈Dn}.)