AL-Rafidain Journal of Computer Sciences and Mathematics

The basis number, b(G) ,of a graph G is defined to be the smallest positive integer k such that G has a k-fold basis for its cycle space. We investigate an upper bound for .It is proved that, if and  are connected vertex-disjoint graphs and each has a spanning tree of vertex degree not more than 4, then  
The basis number of quadruple join of paths, are studied. It is proved that
 
 

The basis number b(G) ,of a graph G is defined to be the least positive integer k such that G has a k-fold basis for it’s cycle space. In this research paper,we have studied the basis number of some special graphs for Mycielski’s graph .It is proved that
 
 
 

The basis number, b(G) ,of a graph G is defined to be the smallest positive integer  k such that G has a k-fold basis for its cycle space. We investigate the basis number of semi-strong product of  with a path, a cycle, a star, a wheel and a complete graph.