Upper bounds on the Q-spectral radius of book-free and/or K_s,t-free graphs

2016/12/12 by Qi Kong, Kong, Qi, Ligong Wang +1
Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50 #msc:15A18

paper · pdf · doi:10.48550/arxiv.1612.03514

8 pages

arxiv created 2016/12/12 · arxiv updated 2016/12/13

Abstract

In this paper, we prove two results about the signless Laplacian spectral radius q(G) of a graph G of order n with maximum degree Δ. Let B_n=K₂+K_n denote a book, i.e., the graph B_n consists of n triangles sharing an edge. (1) Let 1< k≤ l< Δ< n and G be a connected \B_k+1,K_2,l+1\-free graph of order n with maximum degree Δ. Then q(G)≤ (1)/(4)[3Δ+k-2l+1+√(3Δ+k-2l+1)²+16l(Δ+n-1). with equality holds if and only if G is a strongly regular graph with parameters (Δ, k, l). (2) Let s≥ t≥ 3, and let G be a connected K_s,t-free graph of order n (n≥ s+t). Then q(G)≤ n+(s-t+1)^1/tn^1-1/t+(t-1)(n-1)^1-3/t+t-3.

Related

• Maximizing the signless Laplacian spectral radius of some theta graphs
• Maximum degree and spectral radius of graphs in terms of size
• The signless Laplacian spectral radius of subgraphs of regular graphs
• A sharp upper bound on the spectral radius of θ(1,3,3)-free graphs with given size
• The maximum spectral radius of θ_1,3,3-free graphs with given size