Domination and irredundance in cubic graphs

Discrete Mathematics

Volumn 167-168, Issue , 1997, Pages 205-214

  Cockayne, E J ^a   Mynhardt, C M ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b UNIVERSITY OF SOUTH AFRICA   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039382472     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(96)00229-4     Document Type: Article

References (15)

1. R.B. Allan and R. Laskar, On domination and independent domination numbers of a graph, Discrete Math. 23 (1978) 73-76.
2. C. Barefoot, F. Harary and K.F. Jones, What is the difference between the domination and independent domination numbers of a cubic graph? Graphs Combin. 7 (1991) 205-208.
3. C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1973).
4. B. Bollobás and E.J. Cockayne, Graph-theoretic parameters concerning domination, independence and irredundance, J. Graph Theory 3 (1979) 241-249.
5. E.J. Cockayne, O. Favaron, C. Payan and A.G. Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (1981) 249-258.
6. E.J. Cockayne, S.T. Hedetniemi and D.J. Miller, Properties of hereditary hypergraphs and middle graphs, Canad. Math. Bull. 21 (1978) 461-468.
7. E.J. Cockayne and C.M. Mynhardt, Independence and domination in 3-connected cubic graphs, J. Combin. Math. Combin. Comput. 10 (1991) 173-182.
8. O. Favaron, Stability, domination and irredundance in graphs, J. Graph Theory 10 (1986) 429-438.
9. O. Favaron, Two relations between the parameters of independence and irredundance, Discrete Math. 70 (1988) 17-20.
10. M.A. Henning and P.J. Slater, Inequalities relating domination parameters in cubic graphs, Discrete Math. 158 (1996) 87-98.
11. M.S. Jacobson and K. Peters, Chordal graphs and upper irredundance, upper domination and independence, Discrete Math. 86 (1990) 59-69.
12. M.S. Jacobson and K. Peters, A note on graphs which have upper irredundance equal to independence, Discrete Appl. Math. 44 (1993) 91-97.
13. S. Mitchell and S.T. Hedetniemi, Independent domination in trees, Proc. 8th S.E. Conf. on Combinatorics, Graph Theory and Computing (1977) 489-509.
14. C.M. Mynhardt, On the difference between the domination and independent domination numbers of cubic graphs, in: Y. Alavi et al., (eds.) Graph Theory, Combinatorics and Applications: Proc. 6th Internat. Conf. on the Theory and Applications of Graphs (1991) 939-947.
15. J. Žerovnik and J. Oplerova, A counterexample to conjecture of Barefoot, Harary and Jones, Graphs Combin. 9 (1993) 205-207.