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.
© de Gruyter