Keywords : Cycle space


The Basis Number of Quadruple Join of Graphs

Ghassan T. Marougi; Raghad A. Mustafa

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 1, Pages 27-34
DOI: 10.33899/csmj.2012.163685

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
 
 

On the Basis Number of Some Special Graphs for Mycielski’s Graph

Ghassan T. Marougi; Raghad A. Mustafa

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 105-124
DOI: 10.33899/csmj.2011.163654

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
 
 
 

On The Basis Number Of Semi-Strong Product Of With Some Special Graphs

Ghassan T. Marougi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 3, Pages 173-181
DOI: 10.33899/csmj.2009.163831

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.