2024/11/18 by Liu, Yuxiang, Wang, Ligong, Jia, Xiaolong
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2411.11557
The Q-index of graph G is the largest eigenvalue of the signless Laplacian matrix of G. Wang [Discrete Appl. Math. 356(2024)] proved the sharp upper bounds on the Q-index of leaf-free graphs with given size and characterized the corresponding extremal graphs. A graph is 2 leaves-free if it has no two pendent vertices. In this paper, we give sharp upper bounds on the Q-index of 2 leaves-free graphs with given size and characterize the corresponding extremal graphs.