UPPER AND LOWER BOUNDS OF THE BASIS NUMBER OF KRONECKER PRODUCT OF A WHEEL WITH A PATH AND A CYCLE | Zendy

Ayhan khalil | Zendy; Ghassan T. Marougi | Zendy

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UPPER AND LOWER BOUNDS OF THE BASIS NUMBER OF KRONECKER PRODUCT OF A WHEEL WITH A PATH AND A CYCLE

Author(s) -

Ayhan khalil,

Ghassan T. Marougi

Publication year - 2007

Publication title -

mağallaẗ al-tarbiyaẗ wa-al-ʻilm

Language(s) - English

Resource type - Journals

eISSN - 2664-2530

pISSN - 1812-125X

DOI - 10.33899/edusj.2007.5777

Subject(s) - basis (linear algebra) , cycle basis , kronecker product , mathematics , combinatorics , product (mathematics) , graph , path (computing) , upper and lower bounds , integer (computer science) , kronecker delta , discrete mathematics , geometry , computer science , mathematical analysis , physics , graph power , quantum mechanics , line graph , programming language

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 upper and lower bounds of the basis number of Kronecker product of a wheel with a path and a cycle. It is proved that 4 ) ( 3 ≤ ⊗ ≤ n m P W b 4 , ≥ m and 3 ≥ n , and 5 ) ( 3 ≤ ⊗ ≤ n m C W b , 4 ≥ m , 3 ≥ n . UPPER AND LOWER BOUNDS OF THE BASIS... 65

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