Ordering the maxima of L-index and Q-index: Graphs with given size and diameter

The L-index (resp. Q-index) of a graph G is the largest eigenvalue of the Laplacian matrix (resp. signless Laplacian matrix) of G. Very recently, Lou, Guo and Wang [6] determined the graph with fixed size and diameter having the maximum Q-index (resp. L-index). As a continuance of their result, in t...

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Bibliographic Details
Published in:Linear algebra and its applications 2022-11, Vol.652, p.18-36
Main Authors: Jia, Huiming, Li, Shuchao, Wang, Shujing
Format: Article
Language:English
Subjects:
Diameter
L-index
Q-index
Size
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Summary:The L-index (resp. Q-index) of a graph G is the largest eigenvalue of the Laplacian matrix (resp. signless Laplacian matrix) of G. Very recently, Lou, Guo and Wang [6] determined the graph with fixed size and diameter having the maximum Q-index (resp. L-index). As a continuance of their result, in this paper we order all the graphs with given size and diameter from the second to the (⌊d2⌋+1)th via their Q-indices. Consequently, we identify all the graphs of given size and diameter from the second to the ⌊d2⌋th via their L-indices. Furthermore, the graph of given size and diameter with at least one cycle having the largest Q-index is also characterized.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2022.06.028