k-Perfect geodominating sets in graphs

• Autorzy: Mojdeh D. A. , Rad N. J.
• Języki publikacji: EN

Abstrakty

EN

A perfect geodominating set in a graph G is a geodominating set S such that any vertex v ∈ V(G)\S is geodominated by exactly one pair of vertices of S. A k-perfect geodominating set is a geodominating set S such that any vertex v ∈ V(G)\S is geodominated by exactly one pair x, y of vertices of S with d(x, y) = k. We study perfect and k-perfect geodomination numbers of a graph G.

Słowa kluczowe

EN

geodominating set; perfect geodomination number; pendant vertex; pendant edge

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2007
• Tom: Vol. 27, no. 1
• Strony: 51--57
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Mojdeh D. A.

autor

Rad N. J.

• University of Mazandaran, Department of Mathematics, Babolsar, IRAN, P.O. Box 47416-1467,

Bibliografia

• [1] G. Chartrand, F. Harary, P. Zhang, Geodetic sets in graphs, Discussiones Mathematicae Graph Theory 20 (2000), 129-138.
• [2] G. Chartrand, F. Harary, H.C. Swart, P. Zhang, Geodomination in graphs, Bull ICA 31 (2001), 51-59.
• [3] G Chartrand, P. Zhang, The forcing geodetic number of a graph, Discuss. Math. Graph Theory 19 (1999), 45-58.
• [4] D. Donovan, E.S. Mahmoodian, C. Ramsay, A.P. Street, Defining sets in combinatorics: a survey, in surveys in combinatorics. Lecture Notes in Mathematics, eds. Wensley Cambridge University Press, 2003, 113-174.
• [5] R. Muntean, P. Zhang, k-Geodomination in Graphs, ARS Combinatorica 63 (2002), 33-47.
• [6] R. Muntean, P. Zhang, On geodomination in graphs, Congressus Numerantium 143 (2000), 161-174.