Weak signed Roman k-domatic number of a graph

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Volkmann Lutz

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Journal Paper

Paper Information

Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2022 | Volume:7 | Issue:1 Page(s): 17-27

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Title

Weak signed Roman k-domatic number of a graph

Author(s)

Volkmann Lutz | Issue Writer Certificate

Keywords

weak signed Roman k-dominating function

weak signed Roman kdomination number

weak signed Roman k-domatic number

Abstract

Let k 1 be an integer. A weak signed Roman k-dominating function on a graph G is a function f: V (G)! f1; 1; 2g such that P u2N[v] f(u) k for every v 2 V (G), where N[v] is the closed neighborhood of v. A set ff1; f2; : : :; fdg of distinct weak signed Roman k-dominating functions on G with the property that Pd i=1 fi(v) k for each v 2 V (G), is called a weak signed Roman k-dominating family (of functions) on G. The maximum number of functions in a weak signed Roman kdominating family on G is the weak signed Roman k-domatic number of G, denoted by d k wsR (G). In this paper we initiate the study of the weak signed Roman k-domatic number in graphs, and we present sharp bounds for d (G). In addition, we determine the weak signed Roman k-domatic number of some graphs.

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APA: Copy

Volkmann, Lutz. (2022). Weak signed Roman k-domatic number of a graph. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 7(1), 17-27. SID. https://sid.ir/paper/704514/en

Vancouver: Copy

Volkmann Lutz. Weak signed Roman k-domatic number of a graph. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION[Internet]. 2022;7(1):17-27. Available from: https://sid.ir/paper/704514/en

IEEE: Copy

Lutz Volkmann, “Weak signed Roman k-domatic number of a graph,” COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, vol. 7, no. 1, pp. 17–27, 2022, [Online]. Available: https://sid.ir/paper/704514/en

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