Uniform supertrees with extremal spectral radii  

作　　者：Wen-Huan WANG Ling YUAN 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Frontiers of Mathematics in China》2020年第6期1211-1229,共19页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11871040,11001166).

摘　　要：A supertree is a connected and acyclic hypergraph.We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees.First,by using the matching polynomials of supertrees,a new and useful grafting operation is proposed for comparing the spectral radii of supertrees,and its applications are shown to obtain the supertrees with the extremal spectral radi among some kinds of r-uniform supertrees.Second,the supertree with the third smallest spectral radius among the r-uniform supertrees is deduced.Third,among the r-uniform supertrees with a given maximum degree,the supertree with the smallest spectral radius is derived.At last,among the r-uniform starlike supert rees,the supertrees with the smallest and the largest spectral radii are characterized.

关 键 词：HYPERGRAPH spectral radius SUPERTREE matching polynomial 

分 类 号：O17[理学—数学]