Roman k-tuple Domination in Graphs

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KAZEMI ADEL P.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS Year:2020 | Volume:15 | Issue:2 Page(s): 101-115

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Title

Roman k-tuple Domination in Graphs

Author(s)

KAZEMI ADEL P. | Issue Writer Certificate

Keywords

Roman k

tuple domination number

Roman k

tuple graph

Tuple domination number

Tuple total domination number

Abstract

For any integer k ≥ 1 and any graph G = (V, E) with minimum degree at least k − 1, we define a function f: V → {0, 1, 2} as a Roman k-tuple dominating function on G if for any vertex v with f(v) = 0 there exist at least k and for any vertex v with f(v) ̸ = 0 at least k − 1 vertices w in its neighborhood with f(w) = 2. The minimum weight of a Roman k-tuple dominating function f on G is called the Roman k-tuple domination number of the graph where the weight of f is f(V ) = ∑ v∈ V f(v). In this paper, we initiate to study the Roman k-tuple domination number of a graph, by giving some tight bounds for the Roman k-tuple domination number of a garph, the Mycieleskian of a graph, and the corona graphs. Also finding the Roman k-tuple domination number of some known graphs is our other goal. Some of our results extend these one given by Cockayne and et al. [1] in 2004 for the Roman domination number.

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APA: Copy

KAZEMI, ADEL P.. (2020). Roman k-tuple Domination in Graphs. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 15(2), 101-115. SID. https://sid.ir/paper/749605/en

Vancouver: Copy

KAZEMI ADEL P.. Roman k-tuple Domination in Graphs. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2020;15(2):101-115. Available from: https://sid.ir/paper/749605/en

IEEE: Copy

ADEL P. KAZEMI, “Roman k-tuple Domination in Graphs,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 15, no. 2, pp. 101–115, 2020, [Online]. Available: https://sid.ir/paper/749605/en

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