We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the q...We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including integral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.展开更多
基金Supported by National Natural Science Foundation of China(Nos.11971274,12061074,11671344).
文摘We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including integral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.
