2016/10/27 by Qi Kong, Kong, Qi, Ligong Wang +1
Chemistry · Computer Science · Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C50 #msc:15A18
paper · pdf · doi:10.48550/arxiv.1610.08855
9 pages, 2 figures, 1 table
arxiv created 2016/10/27 · openalex publication_date 2016/10/27 · arxiv updated 2016/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let q(H) be the signless Laplacian spectral radius of a graph H. In this paper, we prove that 1. Let H be a proper subgraph of a Δ-regular graph G with n vertices and diameter D. Then 2Δ- q(H)>(1)/(n(D-(1)/(4))). 2. Let H be a proper subgraph of a k-connected Δ-regular graph G with n vertices, where k≥ 2. Then 2Δ-q(H)>\frac2(k-1)22(n-Δ)(n-Δ+2k-4)+(n+1)(k-1)2. Finally, we compare the two bounds. We obtain that when k>2√(((n-Δ)(n+Δ-4))/(n(4D-3)-2))+1, the second bound is always better than the first. On the other hand, when k<(2(n-Δ))/(√(n(4D-3)-2))+1, the first bound is always better than the second.