Operations Research Transactions ›› 2013, Vol. 17 ›› Issue (2): 81-88.

• Original Articles • Previous Articles     Next Articles

The least eigenvalue of graphs whose complements are 2-vertex or 2-edge connected

YU Guidong1,2,FAN Yizheng1,*   

  1. 1. School of Mathematical Sciences, Anhui University, Hefei 230601, China 2. School of Mathematics and Computation Sciences, Anqing Normal College, Anqing 246011, Anhui, China
  • Received:2012-05-03 Online:2013-06-15 Published:2013-06-15

Abstract: The least eigenvalue of a graph is defined as the least eigenvalue of the adjacency matrix of the graph, which is an important algebraic parameter on characterizing structural property of graphs. In this paper we characterize the unique graph with the minimum least eigenvalue among all graphs of fixed order whose complements are 2-vertex connected or 2-edge connected, and present a lower bound for the least eigenvalue of such graphs.

Key words: graph, 2-vertex connected, 2-edge connected, adjacency matrix, least eigenvalue

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