The Basis Number of Quadruple Join of Graphs

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