Abstract
For a simple undirected graph G with fixed size m ≥ 2k(k ∈ Z+)and maximum degree Δ(G)≤ m-k,we give an upper bound on the signless Laplacian spectral radius q(G)of G.For two connected graphs G1 and G2 with size m ≥ 8,employing this upper bound,we prove that q(G1)＞q(G2)if Δ(G1)＞Δ(G2)+1 and Δ(G1)≥ m/2+2.For triangle-free graphs,we prove two stronger results.As an application,we completely characterize the graph with maximal signless Laplacian spectral radius among all graphs with size m and circumference c for m ≥ max{2c,c+9},which partially answers the question proposed by Chen et al.in[Linear Algebra Appl.,2022,645:123-136].
基金项目
National Natural Science Foundation of China(12071411)
National Natural Science Foundation of China(12171222)
NETL
NSTL
万方数据