Random walks on complete multipartite graphs

Xiao Chang, Hao Xu
2015 Pure and Applied Mathematics Quarterly  
Let G n be a simple graph with n vertices. Gutman and Wagner founded the theory of random graphs, they introduced the matching energy of the graph G n , which was defined as the sum of the absolute values of the eigenvalues of the matching polynomial of the graph G n . For the Erdös-Rényi type random graph G n,p of order n with a fixed probability p, where p is a real number greater than zero and less than 1, that is, the graph G on n vertices by connecting two vertices with probability p(e),
more » ... probability p(e), and each edge is independent of other one. Chen, Li and Lian solved a conjecture proposed by Gutman and Wagner, that is, the expectation of the matching energy of G n,p converges to a certain number associated with n and p almost surely. But they only did the result for random bipartite graphs. In this paper, we give some lower bounds for the matching energy of random bipartite graphs. And then we will use Chen et al's method to generalize this conclusion to any random multipartite graphs.
doi:10.4310/pamq.2015.v11.n3.a1 fatcat:xglb7na3yfe4bem544qwon5ase