摘要
A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)
A k-cyclic graph is a connected graph of order n and size n ＋ k - 1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the（combinatorial） Laplacian.
基金
Supported by the National Natural Science Foundation of China（11171273）
Supported by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical Uni- versity（Z2016170）
