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Spectral properties of a class of unicyclic graphs
#MMPMID28529433
Du Z
J Inequal Appl
2017[]; 2017
(1
): 96
PMID28529433
show ga
The eigenvalues of G are denoted by [Formula: see text], where n is the order of
G. In particular, [Formula: see text] is called the spectral radius of G,
[Formula: see text] is the least eigenvalue of G, and the spread of G is defined
to be the difference between [Formula: see text] and [Formula: see text]. Let
[Formula: see text] be the set of n-vertex unicyclic graphs, each of whose
vertices on the unique cycle is of degree at least three. We characterize the
graphs with the kth maximum spectral radius among graphs in [Formula: see text]
for [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula:
see text], and [Formula: see text] if [Formula: see text], and the graph with
minimum least eigenvalue (maximum spread, respectively) among graphs in [Formula:
see text] for [Formula: see text].
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