ON GRAPHS WITH THREE DISTINCT LAPLACIAN EIGENVALUES  

作　　者：Wang Yi Fan Yizheng Tan Yingying 

机构地区：[1]School of Math. and Comput. Sci., Anhui Univ., Hefei 230039, China. [2]Dept. of Math. and Phys., Anhui Institute of Architecture and Industry, Hefei 230022, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2007年第4期478-484,共7页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the Anhui Provincial Natural Science Foundation(050460102);National Natural Science Foundation of China(10601001,10571163);NSF of Department of Education of Anhui Province(2004kj027,2005kj005zd);Foundation of Anhui Institute of Architecture and Industry(200510307);Foundation of Mathematics Innovation Team of Anhui University;Foundation of Talents Group Construction of Anhui University

摘　　要：In this paper, an equivalent condition of a graph G with t （2≤ t ≤n） distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular （necessarily be strongly regular）, an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.In this paper, an equivalent condition of a graph G with t （2≤ t ≤n） distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular （necessarily be strongly regular）, an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.

关 键 词：Laplacian matrix SPECTRUM Laplacian integral strongly regular graph. 

分 类 号：O157.5[理学—数学]