On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles

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DEHGARDI NASRIN

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Journal Paper

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Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2021 | Volume:6 | Issue:2 Page(s): 315-324

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Title

On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles

Author(s)

DEHGARDI NASRIN | Issue Writer Certificate

Keywords

2-rainbow dominating function

2-rainbow domination number

outer independent 2-rainbow dominating function

outer independent 2-rainbow domination number

Cartesian product

Abstract

Let G be a graph. A 2-rainbow dominating function (or 2-RDF) of G is a function f from V (G) to the set of all subsets of the set f1; 2g such that for a vertex v 2 V (G) with f(v) =; , the condition S u2NG(v) f(u) = f1; 2g is ful lled, where NG(v) is the open neighborhood of v. The weight of 2-RDF f of G is the value! (f): = P v2V (G) jf(v)j. The 2-rainbow domination number of G, denoted by r2(G), is the minimum weight of a 2-RDF of G. A 2-RDF f is called an outer independent 2-rainbow dominating function (or OI2-RDF) of G if the set of all v 2 V (G) with f(v) =; is an independent set. The outer independent 2-rainbow domination number oir2(G) is the minimum weight of an OI2-RDF of G. In this paper, we obtain the outer independent 2-rainbow domination number of Pm Pn and Pm Cn. Also we determine the value of oir2(Cm2Cn) when m or n is even.

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APA: Copy

DEHGARDI, NASRIN. (2021). On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 6(2), 315-324. SID. https://sid.ir/paper/704542/en

Vancouver: Copy

DEHGARDI NASRIN. On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION[Internet]. 2021;6(2):315-324. Available from: https://sid.ir/paper/704542/en

IEEE: Copy

NASRIN DEHGARDI, “On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles,” COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, vol. 6, no. 2, pp. 315–324, 2021, [Online]. Available: https://sid.ir/paper/704542/en

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