| On the Least Eigenvalue of Graphs with Cut Vertices |
| Received:November 09, 2008 Revised:May 22, 2009 |
| Key Words:
adjacency matrix least eigenvalue minimizing graph cut vertex.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071002), Key Project of Chinese Ministry of Education (Grant No.210091), Anhui Provincial Natural Science Foundation (Grant No.10040606Y33), Anhui University Innovation Team Project (Grant No.KJTD001B), Project of Anhui Province for Young Teachers Research Support in Universities (Grant No.2008JQl021), Project of Anhui Province for Excellent Young Talents in Universities (Grant No.2009SQRZ017ZD) and the Natural Science Foundation of Department of Education of Anhui Province (Grant No.KJ2010B136). |
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| Abstract: |
| Let ${\mathscr{S}}$ be a certain set of graphs. A graph is called a minimizing graph in the set ${\mathscr{S}}$ if its least eigenvalue attains the minimum among all graphs in ${\mathscr{S}}$. In this paper, we determine the unique minimizing graph in ${\mathscr {G}}_n$, where ${\mathscr {G}}_n$ denotes the set of connected graphs of order $n$ with cut vertices. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.001 |
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