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

Journal of inequalities and applications

Xiaodan Chen¹ 

关键词: number of closed walks;    Estrada index;    Zagreb indices;    maximum degree;    degree sequence;   

DOI  :  10.1186/1029-242X-2014-199

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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 known results obtained by using the algebraic techniques. MSC:05C50, 94C15, 05C38.

【 授权许可】

CC BY