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Let k be a positive integer, and let G be a simple graph with vertex set V(G). A Roman
k-dominating function on G is a function f:V(G)→{0,1,2} such that every
vertex u for which f(u)=0 is adjacent to at least k vertices v_1,v_2,…,v_k with
f(v_i)=2 for i=1,2,…,k. The weight of a Roman k-dominating function is the value
f(V(G))=∑{u∈V(G)}f(u). The minimum weight of a Roman k-dominating function on a
graph G is called the Roman k-domination number γ_{kR}(G) of G. Note that the
Roman 1-domination number γ_{1R}(G) is the usual Roman domination number
γ_R(G). In this paper, we investigate the properties of the Roman k-domination
number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M.
Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.
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참고문헌 (10)
참고문헌 신청
C. S. ReVelle / 2000 / Defendens imperium romanum: a classical problem in military strategy / Amer. Math. Monthly 107 (7) : 585 ~ 594
E. J. Cockayne / 2004 / Roman domination in graphs / Discrete Math. 278 (1) : 11 ~ 22
E. J. Cockayne / 2005 / Protection of a graph / Util. Math. 67 : 19 ~ 32
E. W. Chambers / 2007 / Extremal problems for Roman domination
I. Steward / 1999 / Defend the Roman Empire / Sci. Amer. 281 : 136 ~ 139
E. J. Cockayne / 2004 / Roman domination in graphs / Discrete Math. 278 (1) : 11 ~ 22
E. J. Cockayne / 2005 / Protection of a graph / Util. Math. 67 : 19 ~ 32
E. W. Chambers / 2007 / Extremal problems for Roman domination
I. Steward / 1999 / Defend the Roman Empire / Sci. Amer. 281 : 136 ~ 139
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