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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Maximum Spectral Radius of Graphs with Connectivity at Most k and Minimum Degree at Least δ
verfasst von : Hongliang Lu, Yuqing Lin
Erschienen in: Combinatorial Algorithms
Verlag: Springer Berlin Heidelberg
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Li, Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most
k
, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order
n
with
κ
(
G
) ≤
k
and showed that among those graphs, the maximum spectral radius is obtained uniquely at
$K_k^n$
, which is the graph obtained by joining
k
edges from
k
vertices of
K
n
− 1
to an isolated vertex. In this paper, we study the spectral radius of graphs of order
n
with
κ
(
G
) ≤
k
and minimum degree
δ
(
G
) ≥
k
. We show that among those graphs, the maximum spectral radius is obtained uniquely at
K
k
+ (
K
δ
−
k
+ 1
∪
K
n
−
δ
− 1
).