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The Least Algebraic Connectivity of Graphs

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  • Guisheng Jiang
  • Guidong Yu
  • Jinde Cao

Abstract

The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all graphs whose complements are unicyclic graphs, but not stars adding one edge, respectively.

Suggested Citation

  • Guisheng Jiang & Guidong Yu & Jinde Cao, 2015. "The Least Algebraic Connectivity of Graphs," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-9, October.
    • Handle: RePEc:hin:jnddns:756960
    DOI: 10.1155/2015/756960
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