摘要
Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.
Let G(V,E) be a unicyclic graph,Cm be a cycle of length m and Cm G,and ui ∈ V(Cm).The G-E(Cm) are m trees,denoted by Ti,i = 1,2,...,m.For i = 1,2,...,m,let eui be the excentricity of ui in Ti andec = max{eui:i = 1,2,...,m}.Let k = ec+1.For j = 1,2,...,k-1,letδij = max{dv:dist(v,ui) = j,v ∈ Ti},δj = max{δij:i = 1,2,...,m},δ0 = max{dui:ui ∈ V(Cm)}.ThenIf G≌ Cn,then the equality holds,where λ1(G) is the largest eigenvalue of the adjacency matrix of G.
基金
Foundation item： the National Natural Science Foundation of China （No. 10861009）.
