摘要
连通图G的距离谱半径是其距离矩阵的最大特征值.为了刻画五角链距离谱半径达到最大值和最小值时的极图结构,通过引入图的变换,结合代数图论相关知识,找到了五角链距离谱的变化规律,从而得出在所有含有n个正五边形的五角链中,距离谱半径最小的极图为第一类五角链L_(n),距离谱半径最大的极图为第二类五角链T_(n).
The distance spectral radius of a connected graph G is the largest eigenvalue of its distance matrix.In order to describe the extremal structure of pentagonal chains with the maximum and minimum distance spectral radius,the variation law of distance spectrum of pentagonal chains is found by introducing the graph transformation and combining the knowledge of algebraic graph theory.It is concluded that among all pentagonal chains with n regular pentagons,the extremal graph with minimum distance spectral radius is thefirst kind of pentagonal chain L_(n),and the extremal graph with maximum distance spectral radius is the second kind of pentagonal chain T_(n).
作者
吴一凡
王广富
WU Yi-fan;WANG Guang-fu(School of Science,East China Jiaotong University,Nanchang 330013,China)
出处
《数学的实践与认识》
2022年第8期226-241,共16页
Mathematics in Practice and Theory
基金
国家自然科学基金(11861032,11961026)
江西省自然科学基金(20202BABL201010)。
关键词
五角链
距离谱半径
距离矩阵
极图
Pentagonal chains
distance spectral radius
distance matrix
extremal graphs
