【摘要】 设G为n阶简单连通图,V(G)为G的顶点集,E(G)为G的边集,du表示顶点u的度,Tu表示顶点u的2-度,μ(G)表示图G的Laplician谱半径。该文证明了μ(G)≤max{d2u+d2v+Tu+Tv｜uv∈E(G)}.特别,若G为偶图,则min{d2u+d2v+Tu+Tv|uv∈E(G)}≤μ(G)≤max{d2u+d2v+Tu+Tv|uv∈E(G)}.更多还原

【Abstract】 Let G be a simple connected graph with n vertices. Let du and Tu denote the degree and 2-degree of the vertex u, respectively, μ(G) denote the Laplacian spectral radius of G. In this paper, we proveμ(G)≤max{d2u+d2v+Tu+Tv|uv∈E(G)}.Moreover, if G is a bipartite graph, thenmin{d2u+d2v+Tu+Tv|uv∈E(G)}≤μ(G)≤max{d2u+d2v+Tu+Tv|uv∈E(G)},where if G is a semiregular graph, the equality holds.更多还原