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Bondage number of strong product of two paths.
- Source :
- Frontiers of Mathematics in China; Apr2015, Vol. 10 Issue 2, p435-460, 26p
- Publication Year :
- 2015
-
Abstract
- The bondage number b( G) of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers m ⩾ 2 and n ⩾ 2, b( P ⊠ P) = 7 − r( m) − r( n) if ( r( m), r( n)) = (1, 1) or (3, 3), 6 − r( m) − r( n) otherwise, where r( t) is a function of positive integer t, defined as r( t) = 1 if t ≡ 1 (mod 3), r( t) = 2 if t ≡ 2 (mod 3), and r( t) = 3 if t ≡ 0 (mod 3). [ABSTRACT FROM AUTHOR]
- Subjects :
- GRAPHIC methods
INTEGERS
NUMERICAL analysis
MATHEMATICAL analysis
EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 16733452
- Volume :
- 10
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Frontiers of Mathematics in China
- Publication Type :
- Academic Journal
- Accession number :
- 100905811
- Full Text :
- https://doi.org/10.1007/s11464-014-0391-5