最小Q-特征值为给定整数的一类图  

A Class of Graphs with a Given Integer as Least Q-eigenvalue

作　　者：沈富强[1] 吴宝丰[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2014年第5期425-428,共4页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11301340;11201303;11101284);上海市自然科学基金资助项目(12ZR1420300)

摘　　要：研究了基于二部图H构造的一类图的最小无符号拉普拉斯特征值,即最小Q-特征值,得到了它的最小Q-特征值的可达上界为1.给出了最小Q-特征值为1的2个必要条件,并构造了最小Q-特征值为1的一类图.另外,给出了利用H∨K1的最小Q-特征值来判断简单图H没有完美匹配的方法,以及图G增加边后最小Q-特征值保持不变的1个充分条件.最后,构造了最小Q-特征值为任意给定的正整数t的一类图.When His a bipartite graph,the least signless Laplacian eigenvalue(the least Q-eigenvalue)of a class of graphs constructed by H was studied.It was shown that the sharp upper bound of the least Qeigenvalue of the class of graphs is 1.Moreover,two necessary conditions were given for the graphs whose least Q-eigenvalue is equal to 1,and a class of graphs was constructed which have eigenvalue 1 as their least Qeigenvalue.Also,a method was presented for checking agraph H without a perfect matching by using the least Q-eigenvalue of H∨K1,and a sufficient condition was given when adding edges without changing the least Qeigenvalue.At last,a class of graphs were constructed which have least Q-eigenvalue t,where t is a given positive integer.

关 键 词：无符号拉普拉斯矩阵 最小Q-特征值 界 完美匹配 

分 类 号：O157.5[理学—数学]