Quasiperfect domination in triangular lattices

• Autorzy: Italo J. Dejter
• Języki publikacji: EN

Abstrakty

EN

A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex ($d_v$ ∈ {1,2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3,6} and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form $K_ν$, where ν ∈ {1,2,3} depends only on S.

Słowa kluczowe

EN

perfect dominating set; quasiperfect dominating set; triangular lattice

Kategorie tematyczne

• 68R10: Graph theory (including graph drawing)
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 1
• Strony: 179-198

Daty

wydano

2009

Twórcy

autor

Italo J. Dejter

• University of Puerto Rico, Rio Piedras, PR 00931-3355

Bibliografia

• [1] D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs, Appl. Discrete Math, eds. R.D. Ringeisen and F.S. Roberts (SIAM, Philadelphia, 1988) 189-199.
• [2] I.J. Dejter, Perfect domination of regular grid graphs, Australasian J. Combin. 92 (2008) 99-114.
• [3] I.J. Dejter and A.A. Delgado, Perfect dominating sets in grid graphs, JCMCC 70 (2009), to appear.
• [4] L. Fejes Tóth, Regular Figures (Pergamon Press, Oxford UK, 1964).
• [5] J. Kratochvil and M. Krivánek, On the Computational Complexity of Codes in Graphs, in: Proc. MFCS 1988, LNCS 324 (Springer-Verlag), 396-404.
• [6] C. Thomassen, On the Nelson unit distance coloring problem, Amer. Math. Monthly 106 (1999) 850-853, doi: 10.2307/2589618.

Identyfikatory

DOI

10.7151/dmgt.1439