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On the intersection number of a graph
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E. E. Marenich
Published/Copyright:
December 10, 2007
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
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- A multivariate Poisson theorem for the number of solutions close to given vectors of a system of random linear equations
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- On the intersection number of a graph
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Articles in the same Issue
- Properties of the output sequence of a simplest 2-linear shift register over Z2n
- A multivariate Poisson theorem for the number of solutions close to given vectors of a system of random linear equations
- Critical multitype branching processes in a random environment
- On the intersection number of a graph
- Generalised Pascal pyramids and their reciprocals
- On identical transformations in commutative semigroups
