Bounds on the number of closed walks in a graph and its applications

Xiaodan Chen, Jianguo Qian
2014 Journal of Inequalities and Applications  
Using graph-theoretical techniques, we establish an inequality regarding the number of walks and closed walks in a graph. This inequality yields several upper bounds for the number of closed walks in a graph in terms of the number of vertices, number of edges, maximum degree, degree sequence, and the Zagreb indices of the graph. As applications, we also present some new upper bounds on the Estrada index for general graphs, bipartite graphs, trees and planar graphs, some of which improve the
more » ... n results obtained by using the algebraic techniques. MSC: 05C50; 94C15; 05C38
doi:10.1186/1029-242x-2014-199 fatcat:vinozvufcjemle774c4jdm442a