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The least eigenvalue of graphs whose complements are unicyclic | | Yi Wang
; Yi-Zheng Fan
; Xiao-Xin Li
; Fei-Fei Zhang
; | | Date: |
19 May 2013 | | Abstract: | A graph in a certain graph class is called minimizing if the least eigenvalue
of the adjacency matrix of the graph attains the minimum among all graphs in
that class. Bell {it et al.} have characterized the minimizing graphs in the
class of connected graphs of order $n$ and size $m$, whose complements are
either disconnected or contain a clique of order at least $n/2$. In this paper
we discuss the minimizing graphs of a special class of graphs of order $n$
whose complements are connected and contains exactly one cycle (namely the the
class $mathscr {U}^{c}_{n}$ of graphs whose complements are unicyclic), and
characterize the unique minimizing graph in $mathscr {U}^{c}_{n}$ when $n geq
20$. | | Source: | arXiv, 1305.4317 | | Services: | Forum | Review | PDF | Favorites | |
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