The spectral radius of triangle-free graphs. (English) Zbl 1008.05089
Two lower bounds for the spectral radius of the Laplacian matrices of triangle-free graphs are presented. One is in terms of the number of edges and vertices of graphs, and the other is in terms of degrees and average 2-degrees of vertices. Here the average 2-degree of a vertex is the average of the degrees of its neighbours. From the two bounds, interesting corollaries are derived.
Reviewer: Martin Knor (Bratislava)
MSC:
05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
05C35 | Extremal problems in graph theory |