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We find an expression of the intersection number of a graph in terms of the minimum number of complete subgraphs that form a covering of the graph. This provides us with a uniform approach to studying properties of the intersection number of a graph. We distinguish the class of graphs for which the intersection number is equal to the least number of cliques covering the graph. It is proved that the intersection number of a complete r-partite graph 
is equal to the least n such that 
. It is proved that the intersection number of the graph 
is equal to the least n such that 
. Formulas for the intersection numbers of the graphs rC4, r Chain(3), r(C4 + Km), rW5 are obtained.
Received: 2005-April-19
Published Online: 2007-12-10
Published in Print: 2007-12-11
© de Gruyter
