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

作者：Jia, Huiming; Li, Shuchao; Wang, Shujing^*

来源：Linear Algebra and Its Applications, 2022, 652: 18-36.

DOI：10.1016/j.laa.2022.06.028

• L-index
• Q-index
• Size
• 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 this paper we order all the graphs with given size and diameter from the second to the ([d/2] + 1)th via their Q-indices. Consequently, we identify all the graphs of given size and diameter from the second to the [2/d]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.