The graphs with all but two eigenvalues equal to $2$ or $-1$

Jing Li; Deqiong Li; Yaoping Hou

The graphs with all but two eigenvalues equal to $2$ or $-1$

Combinatorics 2018-06-20 v1

Authors: Jing Li , Deqiong Li , Yaoping Hou

Abstract

In this paper, all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from $2$ and $-1$ are determined. These graphs conclude a class of generalized friendship graphs $F_{t,r,k},$ which is the graph of $k$ copies of the complete graph $K_t$ meeting in common $r$ vertices such that $t-r=3.$ Which of these graphs are determined by its spectrum is are also obtained.

Keywords

graph laplacian graph theory bipartite graphs

Cite

@article{arxiv.1806.07260,
  title  = {The graphs with all but two eigenvalues equal to $2$ or $-1$},
  author = {Jing Li and Deqiong Li and Yaoping Hou},
  journal= {arXiv preprint arXiv:1806.07260},
  year   = {2018}
}

Comments

18 pages, 2 figures. arXiv admin note: text overlap with arXiv:1310.6529 by other authors

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