On the basis number of the direct product of graphs
Mohammed M. M. Jaradat · 2003
The basis number b(G) ofagraphGis defined to be the least integer d such that G has a d-fold basis for its cycle space. In this paper we: give an upper bound of the basis number of the direct product of trees; classify the trees with respect to the basis number of the direct product of trees and paths of order greater than or equal to 5; give an upper bound of the basis number of the direct product of bipartite graphs; and investigate the basis number of the direct product of a bipartite graph and a cycle. 1