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On the Second Least Distance Eigenvalue of a Graph
Electronic Journal of Linear Algebra
  • Xueyi Huang, College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang 830046, P.R.China.
  • Qiongxiang Huang, Xinjiang University
  • Lu Lu, Xinjiang University
  • distance matrix,
  • the second least distance eigenvalue,
  • distance cospectral graph.

Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\partial_1(G)\ge\partial_2(G)\ge\cdots\ge\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, the connected graphs with @n􀀀1(G) at least the smallest root of $x^3=3x^2-11x-6 = 0$ are determined. Additionally, some non-isomorphic distance cospectral graphs are given.

Citation Information
Xueyi Huang, Qiongxiang Huang and Lu Lu. "On the Second Least Distance Eigenvalue of a Graph" p. 531 - 538
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