The Signless p-Laplacian Spectral Radius of Graphs with Given Degree Sequences.

In this paper, we consider the spectral radius of signless p-Laplacian of a graph, which is a generalization of the quadratic form of the signless Laplacian matrix for p = 2 . Let π = (d 0 , d 1 , … , d n - 1) be a non-increasing sequence of positive integers and G π the set of graphs with degree sequence π . In this paper, we obtain some transformations for graphs in G π that do not decrease the largest signless p-Laplacian eigenvalue of a graph. Furthermore, if ∑ i = 0 n - 1 d i = 2 n and d 2 ≥ 2 , then we identify the graph maximizing the signless p-Laplacian spectral radius among G π . As an application, we get the extremal graph maximizing the signless p-Laplacian spectral radius among all unicyclic graphs. [ABSTRACT FROM AUTHOR]