Abstract
In [1] C. Barefoot, F. Harary and K. Jones conjectured that for cubic graphs with connectivity three the difference between the domination and independent domination numbers is at most one. We disprove this conjecture and give an exhaustive answer to the question: “What is the difference between the domination and independent domination numbers for cubic graphs with given connectivity?”
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References
Barefoot, F., Jones, K.F.: What is the difference between the domination and independent domination numbers of a cubic graph? Graphs and Combin. 7, 205–208 (1991)
F.: Graph Theory. Reading: Addison-Wesley 1969
Mynhardt, G: On the difference between the domination and independent domination numbers of cubic graphs. Theory of Graphs and Applications, New York: Wiley 1991
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Zverovich, I.E., Zverovich, V.E. Disproof of a Conjecture in the Domination Theory. Graphs and Combinatorics 10, 389–396 (1994). https://doi.org/10.1007/BF02986690
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DOI: https://doi.org/10.1007/BF02986690