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of China (60672160), Shanghai Pujiang Program (06PJ14039), and by the Shanghai Leading Academic Discipline Project(J50101). Electronic Journal of Linear Algebra ISSN 1081-3810

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume

by studying the Perron vector of G , it is shown that type-I-a graphs and type-I-b (resp. type-II-a).. graphs with some specified properties are not λ 1

The work of this author was supported by the NSFC Tianyuan Mathematics Youth Fund (10926086), and in part by Independent Innovation Research Plan of CUP (09CX04004A). ‡ School

The work of this author was Supported by Natural Science Basic Research Project in Shaanxi Province: 2010JQ1016. Electronic Journal of Linear Algebra ISSN 1081-3810 A publication

This work is supported by the National Natural Sci- ence Foundation of China (No 10971137), the National Basic Research Program (973) of China (No 2006CB805900), and a grant of

This work was partially supported by the Ministerio de Ciencia e Innovaci´ on of Spain through grant MTM-2009-09281.. † Departamento de Matem´ aticas, Universidad Carlos III de