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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2019.1
- 수록면
- 515 - 523 (9page)
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Consider a graph G of order n and maximum degree . Let f : V (G) → {0, 1, ... , [/2 ]+1 } be a function that labels the vertices of G. Let B0 = {v in V (G) : f(v) = 0}. The function f is a strong Roman dominating function for G if every v in B0 has a neighbor w such that f(w) >1+[ 1 /2 |N(w) B0} ]. In this paper, we study the bounds on strong Roman domination numbers of the Cartesian product PmPk of paths Pm and paths Pk. We compute the exact values for the strong Roman domination number of the Cartesian product P2Pk and P3Pk. We also show that the strong Roman domination number of the Cartesian product P4Pk is between [ 1/3 (8k-[ k/ 8] +1)] and [ 8k/3] for k> 8, and that both bounds are sharp bounds.
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참고문헌 (4)
참고문헌 신청
M P. Alvarez-Ruiz / 2017 / On the strong Roman domination number of graphs / Dis-crete Appl. Math 231:44~59
E. J. Cockayne / 2004 / Roman domination in graphs / Discrete Math 278:11~22
C. S. ReVelle / 2000 / Defendents imperium romanum : a classical problem in military strategy / Amer. Math. Monthly 107(7):585~594
I. Stewart / 1999 / Defend the roman empire! / Sci. Amer 281(6):136~138
E. J. Cockayne / 2004 / Roman domination in graphs / Discrete Math 278:11~22
C. S. ReVelle / 2000 / Defendents imperium romanum : a classical problem in military strategy / Amer. Math. Monthly 107(7):585~594
I. Stewart / 1999 / Defend the roman empire! / Sci. Amer 281(6):136~138
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